WORST_CASE(Omega(n^1), O(n^4)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^4). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 208 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 79.5 s] (14) BOUNDS(1, n^4) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 216 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 123 ms] (28) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^4). The TRS R consists of the following rules: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) minus(0, Y) -> 0 minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0 ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^4). The TRS R consists of the following rules: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) minus(0, Y) -> 0 minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0 ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^4). The TRS R consists of the following rules: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) minus(0, Y) -> 0 minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0 ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0, s(Y)) -> 0 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) The (relative) TRS S consists of the following rules: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^4). The TRS R consists of the following rules: le(0, Y) -> true [1] le(s(X), 0) -> false [1] le(s(X), s(Y)) -> le(X, Y) [1] minus(0, Y) -> 0 [1] minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) [1] ifMinus(true, s(X), Y) -> 0 [1] ifMinus(false, s(X), Y) -> s(minus(X, Y)) [1] quot(0, s(Y)) -> 0 [1] quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: le(0, Y) -> true [1] le(s(X), 0) -> false [1] le(s(X), s(Y)) -> le(X, Y) [1] minus(0, Y) -> 0 [1] minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) [1] ifMinus(true, s(X), Y) -> 0 [1] ifMinus(false, s(X), Y) -> s(minus(X, Y)) [1] quot(0, s(Y)) -> 0 [1] quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) [0] The TRS has the following type information: le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot 0 :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot true :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot s :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot false :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encArg :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_0 :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_true :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_s :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_false :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_le(v0, v1) -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_ifMinus(v0, v1, v2) -> null_encode_ifMinus [0] encode_quot(v0, v1) -> null_encode_quot [0] le(v0, v1) -> null_le [0] minus(v0, v1) -> null_minus [0] ifMinus(v0, v1, v2) -> null_ifMinus [0] quot(v0, v1) -> null_quot [0] And the following fresh constants: null_encArg, null_encode_le, null_encode_0, null_encode_true, null_encode_s, null_encode_false, null_encode_minus, null_encode_ifMinus, null_encode_quot, null_le, null_minus, null_ifMinus, null_quot ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: le(0, Y) -> true [1] le(s(X), 0) -> false [1] le(s(X), s(Y)) -> le(X, Y) [1] minus(0, Y) -> 0 [1] minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) [1] ifMinus(true, s(X), Y) -> 0 [1] ifMinus(false, s(X), Y) -> s(minus(X, Y)) [1] quot(0, s(Y)) -> 0 [1] quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) [1] encArg(0) -> 0 [0] encArg(true) -> true [0] encArg(s(x_1)) -> s(encArg(x_1)) [0] encArg(false) -> false [0] encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) [0] encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) [0] encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) [0] encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_true -> true [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_false -> false [0] encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) [0] encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) [0] encArg(v0) -> null_encArg [0] encode_le(v0, v1) -> null_encode_le [0] encode_0 -> null_encode_0 [0] encode_true -> null_encode_true [0] encode_s(v0) -> null_encode_s [0] encode_false -> null_encode_false [0] encode_minus(v0, v1) -> null_encode_minus [0] encode_ifMinus(v0, v1, v2) -> null_encode_ifMinus [0] encode_quot(v0, v1) -> null_encode_quot [0] le(v0, v1) -> null_le [0] minus(v0, v1) -> null_minus [0] ifMinus(v0, v1, v2) -> null_ifMinus [0] quot(v0, v1) -> null_quot [0] The TRS has the following type information: le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot 0 :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot true :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot s :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot false :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encArg :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot cons_le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot cons_minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot cons_ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot cons_quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_0 :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_true :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_s :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_false :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot encode_quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot -> 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encArg :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_0 :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_true :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_s :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_false :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_encode_quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_le :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_minus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_ifMinus :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot null_quot :: 0:true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot:null_encArg:null_encode_le:null_encode_0:null_encode_true:null_encode_s:null_encode_false:null_encode_minus:null_encode_ifMinus:null_encode_quot:null_le:null_minus:null_ifMinus:null_quot Rewrite Strategy: INNERMOST ---------------------------------------- (11) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 true => 2 false => 1 null_encArg => 0 null_encode_le => 0 null_encode_0 => 0 null_encode_true => 0 null_encode_s => 0 null_encode_false => 0 null_encode_minus => 0 null_encode_ifMinus => 0 null_encode_quot => 0 null_le => 0 null_minus => 0 null_ifMinus => 0 null_quot => 0 ---------------------------------------- (12) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> quot(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_0 -{ 0 }-> 0 :|: encode_false -{ 0 }-> 1 :|: encode_false -{ 0 }-> 0 :|: encode_ifMinus(z, z', z'') -{ 0 }-> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_ifMinus(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_le(z, z') -{ 0 }-> le(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_minus(z, z') -{ 0 }-> minus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_quot(z, z') -{ 0 }-> quot(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_s(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_true -{ 0 }-> 2 :|: encode_true -{ 0 }-> 0 :|: ifMinus(z, z', z'') -{ 1 }-> 0 :|: z = 2, Y >= 0, z'' = Y, z' = 1 + X, X >= 0 ifMinus(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 ifMinus(z, z', z'') -{ 1 }-> 1 + minus(X, Y) :|: Y >= 0, z = 1, z'' = Y, z' = 1 + X, X >= 0 le(z, z') -{ 1 }-> le(X, Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0 le(z, z') -{ 1 }-> 2 :|: z' = Y, Y >= 0, z = 0 le(z, z') -{ 1 }-> 1 :|: z = 1 + X, X >= 0, z' = 0 le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 minus(z, z') -{ 1 }-> ifMinus(le(1 + X, Y), 1 + X, Y) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0 minus(z, z') -{ 1 }-> 0 :|: z' = Y, Y >= 0, z = 0 minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 quot(z, z') -{ 1 }-> 0 :|: Y >= 0, z' = 1 + Y, z = 0 quot(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 quot(z, z') -{ 1 }-> 1 + quot(minus(X, Y), 1 + Y) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (13) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V2),0,[le(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[ifMinus(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[quot(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[fun1(Out)],[]). eq(start(V1, V, V2),0,[fun2(Out)],[]). eq(start(V1, V, V2),0,[fun3(V1, Out)],[V1 >= 0]). eq(start(V1, V, V2),0,[fun4(Out)],[]). eq(start(V1, V, V2),0,[fun5(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V2),0,[fun6(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]). eq(start(V1, V, V2),0,[fun7(V1, V, Out)],[V1 >= 0,V >= 0]). eq(le(V1, V, Out),1,[],[Out = 2,V = Y1,Y1 >= 0,V1 = 0]). eq(le(V1, V, Out),1,[],[Out = 1,V1 = 1 + X1,X1 >= 0,V = 0]). eq(le(V1, V, Out),1,[le(X2, Y2, Ret)],[Out = Ret,V1 = 1 + X2,Y2 >= 0,V = 1 + Y2,X2 >= 0]). eq(minus(V1, V, Out),1,[],[Out = 0,V = Y3,Y3 >= 0,V1 = 0]). eq(minus(V1, V, Out),1,[le(1 + X3, Y4, Ret0),ifMinus(Ret0, 1 + X3, Y4, Ret1)],[Out = Ret1,V1 = 1 + X3,V = Y4,Y4 >= 0,X3 >= 0]). eq(ifMinus(V1, V, V2, Out),1,[],[Out = 0,V1 = 2,Y5 >= 0,V2 = Y5,V = 1 + X4,X4 >= 0]). eq(ifMinus(V1, V, V2, Out),1,[minus(X5, Y6, Ret11)],[Out = 1 + Ret11,Y6 >= 0,V1 = 1,V2 = Y6,V = 1 + X5,X5 >= 0]). eq(quot(V1, V, Out),1,[],[Out = 0,Y7 >= 0,V = 1 + Y7,V1 = 0]). eq(quot(V1, V, Out),1,[minus(X6, Y8, Ret10),quot(Ret10, 1 + Y8, Ret12)],[Out = 1 + Ret12,V1 = 1 + X6,Y8 >= 0,V = 1 + Y8,X6 >= 0]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[encArg(V3, Ret13)],[Out = 1 + Ret13,V1 = 1 + V3,V3 >= 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[encArg(V4, Ret01),encArg(V5, Ret14),le(Ret01, Ret14, Ret2)],[Out = Ret2,V4 >= 0,V1 = 1 + V4 + V5,V5 >= 0]). eq(encArg(V1, Out),0,[encArg(V6, Ret02),encArg(V7, Ret15),minus(Ret02, Ret15, Ret3)],[Out = Ret3,V6 >= 0,V1 = 1 + V6 + V7,V7 >= 0]). eq(encArg(V1, Out),0,[encArg(V10, Ret03),encArg(V9, Ret16),encArg(V8, Ret21),ifMinus(Ret03, Ret16, Ret21, Ret4)],[Out = Ret4,V10 >= 0,V1 = 1 + V10 + V8 + V9,V8 >= 0,V9 >= 0]). eq(encArg(V1, Out),0,[encArg(V12, Ret04),encArg(V11, Ret17),quot(Ret04, Ret17, Ret5)],[Out = Ret5,V12 >= 0,V1 = 1 + V11 + V12,V11 >= 0]). eq(fun(V1, V, Out),0,[encArg(V13, Ret05),encArg(V14, Ret18),le(Ret05, Ret18, Ret6)],[Out = Ret6,V13 >= 0,V14 >= 0,V1 = V13,V = V14]). eq(fun1(Out),0,[],[Out = 0]). eq(fun2(Out),0,[],[Out = 2]). eq(fun3(V1, Out),0,[encArg(V15, Ret19)],[Out = 1 + Ret19,V15 >= 0,V1 = V15]). eq(fun4(Out),0,[],[Out = 1]). eq(fun5(V1, V, Out),0,[encArg(V17, Ret06),encArg(V16, Ret110),minus(Ret06, Ret110, Ret7)],[Out = Ret7,V17 >= 0,V16 >= 0,V1 = V17,V = V16]). eq(fun6(V1, V, V2, Out),0,[encArg(V20, Ret07),encArg(V19, Ret111),encArg(V18, Ret22),ifMinus(Ret07, Ret111, Ret22, Ret8)],[Out = Ret8,V20 >= 0,V18 >= 0,V19 >= 0,V1 = V20,V = V19,V2 = V18]). eq(fun7(V1, V, Out),0,[encArg(V21, Ret08),encArg(V22, Ret112),quot(Ret08, Ret112, Ret9)],[Out = Ret9,V21 >= 0,V22 >= 0,V1 = V21,V = V22]). eq(encArg(V1, Out),0,[],[Out = 0,V23 >= 0,V1 = V23]). eq(fun(V1, V, Out),0,[],[Out = 0,V25 >= 0,V24 >= 0,V1 = V25,V = V24]). eq(fun2(Out),0,[],[Out = 0]). eq(fun3(V1, Out),0,[],[Out = 0,V26 >= 0,V1 = V26]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(V1, V, Out),0,[],[Out = 0,V27 >= 0,V28 >= 0,V1 = V27,V = V28]). eq(fun6(V1, V, V2, Out),0,[],[Out = 0,V29 >= 0,V2 = V31,V30 >= 0,V1 = V29,V = V30,V31 >= 0]). eq(fun7(V1, V, Out),0,[],[Out = 0,V32 >= 0,V33 >= 0,V1 = V32,V = V33]). eq(le(V1, V, Out),0,[],[Out = 0,V35 >= 0,V34 >= 0,V1 = V35,V = V34]). eq(minus(V1, V, Out),0,[],[Out = 0,V36 >= 0,V37 >= 0,V1 = V36,V = V37]). eq(ifMinus(V1, V, V2, Out),0,[],[Out = 0,V38 >= 0,V2 = V40,V39 >= 0,V1 = V38,V = V39,V40 >= 0]). eq(quot(V1, V, Out),0,[],[Out = 0,V41 >= 0,V42 >= 0,V1 = V41,V = V42]). input_output_vars(le(V1,V,Out),[V1,V],[Out]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(ifMinus(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(quot(V1,V,Out),[V1,V],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,Out),[V1,V],[Out]). input_output_vars(fun1(Out),[],[Out]). input_output_vars(fun2(Out),[],[Out]). input_output_vars(fun3(V1,Out),[V1],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(V1,V,Out),[V1,V],[Out]). input_output_vars(fun6(V1,V,V2,Out),[V1,V,V2],[Out]). input_output_vars(fun7(V1,V,Out),[V1,V],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [le/3] 1. recursive : [ifMinus/4,minus/3] 2. recursive : [quot/3] 3. recursive [non_tail,multiple] : [encArg/2] 4. non_recursive : [fun/3] 5. non_recursive : [fun1/1] 6. non_recursive : [fun2/1] 7. non_recursive : [fun3/2] 8. non_recursive : [fun4/1] 9. non_recursive : [fun5/3] 10. non_recursive : [fun6/4] 11. non_recursive : [fun7/3] 12. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into le/3 1. SCC is partially evaluated into minus/3 2. SCC is partially evaluated into quot/3 3. SCC is partially evaluated into encArg/2 4. SCC is partially evaluated into fun/3 5. SCC is completely evaluated into other SCCs 6. SCC is partially evaluated into fun2/1 7. SCC is partially evaluated into fun3/2 8. SCC is partially evaluated into fun4/1 9. SCC is partially evaluated into fun5/3 10. SCC is partially evaluated into fun6/4 11. SCC is partially evaluated into fun7/3 12. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations le/3 * CE 23 is refined into CE [53] * CE 21 is refined into CE [54] * CE 20 is refined into CE [55] * CE 22 is refined into CE [56] ### Cost equations --> "Loop" of le/3 * CEs [56] --> Loop 26 * CEs [53] --> Loop 27 * CEs [54] --> Loop 28 * CEs [55] --> Loop 29 ### Ranking functions of CR le(V1,V,Out) * RF of phase [26]: [V,V1] #### Partial ranking functions of CR le(V1,V,Out) * Partial RF of phase [26]: - RF of loop [26:1]: V V1 ### Specialization of cost equations minus/3 * CE 15 is refined into CE [57,58,59,60] * CE 17 is refined into CE [61] * CE 18 is refined into CE [62] * CE 19 is refined into CE [63] * CE 16 is refined into CE [64,65] ### Cost equations --> "Loop" of minus/3 * CEs [65] --> Loop 30 * CEs [64] --> Loop 31 * CEs [57] --> Loop 32 * CEs [58,59,60,61,62,63] --> Loop 33 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [30]: [V1-1,V1-V] * RF of phase [31]: [V1] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [30]: - RF of loop [30:1]: V1-1 V1-V * Partial RF of phase [31]: - RF of loop [31:1]: V1 ### Specialization of cost equations quot/3 * CE 24 is refined into CE [66] * CE 26 is refined into CE [67] * CE 25 is refined into CE [68,69,70] ### Cost equations --> "Loop" of quot/3 * CEs [70] --> Loop 34 * CEs [68] --> Loop 35 * CEs [69] --> Loop 36 * CEs [66,67] --> Loop 37 ### Ranking functions of CR quot(V1,V,Out) * RF of phase [34]: [V1/2-1,V1/2-V/2] * RF of phase [36]: [V1-1] #### Partial ranking functions of CR quot(V1,V,Out) * Partial RF of phase [34]: - RF of loop [34:1]: V1/2-1 V1/2-V/2 * Partial RF of phase [36]: - RF of loop [36:1]: V1-1 ### Specialization of cost equations encArg/2 * CE 30 is refined into CE [71] * CE 31 is refined into CE [72] * CE 33 is refined into CE [73] * CE 34 is refined into CE [74,75,76,77,78] * CE 35 is refined into CE [79,80,81] * CE 36 is refined into CE [82,83,84,85,86,87] * CE 32 is refined into CE [88] * CE 28 is refined into CE [89,90,91] * CE 27 is refined into CE [92] * CE 29 is refined into CE [93] ### Cost equations --> "Loop" of encArg/2 * CEs [91] --> Loop 38 * CEs [90] --> Loop 39 * CEs [89] --> Loop 40 * CEs [92,93] --> Loop 41 * CEs [88] --> Loop 42 * CEs [87] --> Loop 43 * CEs [83] --> Loop 44 * CEs [81,82,86] --> Loop 45 * CEs [78] --> Loop 46 * CEs [74] --> Loop 47 * CEs [77,85] --> Loop 48 * CEs [75,80] --> Loop 49 * CEs [76,79,84] --> Loop 50 * CEs [71] --> Loop 51 * CEs [72] --> Loop 52 * CEs [73] --> Loop 53 ### Ranking functions of CR encArg(V1,Out) * RF of phase [38,39,40,41,42,43,44,45,46,47,48,49,50]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [38,39,40,41,42,43,44,45,46,47,48,49,50]: - RF of loop [38:1,38:2,38:3,39:1,39:2,39:3,40:1,40:2,40:3,41:1,41:2,41:3,42:1,43:1,43:2,44:1,44:2,45:1,45:2,46:1,46:2,47:1,47:2,48:1,48:2,49:1,49:2,50:1,50:2]: V1 ### Specialization of cost equations fun/3 * CE 37 is refined into CE [94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119] * CE 38 is refined into CE [120] ### Cost equations --> "Loop" of fun/3 * CEs [99,102,116] --> Loop 54 * CEs [101] --> Loop 55 * CEs [100,117] --> Loop 56 * CEs [95,97,104,106,108,112] --> Loop 57 * CEs [94,98,103,109,111,114,118] --> Loop 58 * CEs [96,105,107,110,113,115,119,120] --> Loop 59 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun2/1 * CE 39 is refined into CE [121] * CE 40 is refined into CE [122] ### Cost equations --> "Loop" of fun2/1 * CEs [121] --> Loop 60 * CEs [122] --> Loop 61 ### Ranking functions of CR fun2(Out) #### Partial ranking functions of CR fun2(Out) ### Specialization of cost equations fun3/2 * CE 41 is refined into CE [123,124,125] * CE 42 is refined into CE [126] ### Cost equations --> "Loop" of fun3/2 * CEs [125] --> Loop 62 * CEs [126] --> Loop 63 * CEs [123,124] --> Loop 64 ### Ranking functions of CR fun3(V1,Out) #### Partial ranking functions of CR fun3(V1,Out) ### Specialization of cost equations fun4/1 * CE 43 is refined into CE [127] * CE 44 is refined into CE [128] ### Cost equations --> "Loop" of fun4/1 * CEs [127] --> Loop 65 * CEs [128] --> Loop 66 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/3 * CE 45 is refined into CE [129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144] * CE 46 is refined into CE [145] ### Cost equations --> "Loop" of fun5/3 * CEs [133] --> Loop 67 * CEs [132,143] --> Loop 68 * CEs [130,131,135,137,138,141] --> Loop 69 * CEs [129,134,136,139,140,142,144,145] --> Loop 70 ### Ranking functions of CR fun5(V1,V,Out) #### Partial ranking functions of CR fun5(V1,V,Out) ### Specialization of cost equations fun6/4 * CE 47 is refined into CE [146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172] * CE 48 is refined into CE [173,174,175,176,177,178,179,180,181,182,183,184] * CE 49 is refined into CE [185,186,187,188,189,190,191,192,193,194,195,196] * CE 50 is refined into CE [197] ### Cost equations --> "Loop" of fun6/4 * CEs [177] --> Loop 71 * CEs [176] --> Loop 72 * CEs [174,175,179,181,184] --> Loop 73 * CEs [173,178,180,182,183] --> Loop 74 * CEs [149,150,151,167,168,169,188,189,190] --> Loop 75 * CEs [147,153,156,162,165,171,186,192] --> Loop 76 * CEs [146,148,152,154,155,157,158,159,160,161,163,164,166,170,172,185,187,191,193,194,195,196,197] --> Loop 77 ### Ranking functions of CR fun6(V1,V,V2,Out) #### Partial ranking functions of CR fun6(V1,V,V2,Out) ### Specialization of cost equations fun7/3 * CE 51 is refined into CE [198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218] * CE 52 is refined into CE [219] ### Cost equations --> "Loop" of fun7/3 * CEs [207] --> Loop 78 * CEs [202,206] --> Loop 79 * CEs [205] --> Loop 80 * CEs [204,217] --> Loop 81 * CEs [199,210] --> Loop 82 * CEs [198,201,203,209,212,214] --> Loop 83 * CEs [200,208,211,213,215,216,218,219] --> Loop 84 ### Ranking functions of CR fun7(V1,V,Out) #### Partial ranking functions of CR fun7(V1,V,Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [220] * CE 2 is refined into CE [221,222,223] * CE 3 is refined into CE [224] * CE 4 is refined into CE [225,226,227,228,229] * CE 5 is refined into CE [230,231,232] * CE 6 is refined into CE [233,234,235,236,237,238] * CE 7 is refined into CE [239,240,241] * CE 8 is refined into CE [242,243,244] * CE 9 is refined into CE [245,246] * CE 10 is refined into CE [247,248,249] * CE 11 is refined into CE [250,251] * CE 12 is refined into CE [252,253] * CE 13 is refined into CE [254,255,256,257] * CE 14 is refined into CE [258,259,260,261] ### Cost equations --> "Loop" of start/3 * CEs [220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261] --> Loop 85 ### Ranking functions of CR start(V1,V,V2) #### Partial ranking functions of CR start(V1,V,V2) Computing Bounds ===================================== #### Cost of chains of le(V1,V,Out): * Chain [[26],29]: 1*it(26)+1 Such that:it(26) =< V1 with precondition: [Out=2,V1>=1,V>=V1] * Chain [[26],28]: 1*it(26)+1 Such that:it(26) =< V with precondition: [Out=1,V>=1,V1>=V+1] * Chain [[26],27]: 1*it(26)+0 Such that:it(26) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [29]: 1 with precondition: [V1=0,Out=2,V>=0] * Chain [28]: 1 with precondition: [V=0,Out=1,V1>=1] * Chain [27]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[31],33]: 3*it(31)+2*s(4)+3 Such that:aux(1) =< V1-Out it(31) =< Out s(4) =< aux(1) with precondition: [V=0,Out>=1,V1>=Out] * Chain [[31],32]: 3*it(31)+2 Such that:it(31) =< Out with precondition: [V=0,Out>=1,V1>=Out+1] * Chain [[30],33]: 3*it(30)+2*s(2)+2*s(4)+1*s(8)+3 Such that:aux(1) =< V1-Out it(30) =< Out aux(4) =< V s(4) =< aux(1) s(2) =< aux(4) s(8) =< it(30)*aux(4) with precondition: [V>=1,Out>=1,V1>=Out+V] * Chain [33]: 2*s(2)+2*s(4)+3 Such that:aux(1) =< V1 aux(2) =< V s(4) =< aux(1) s(2) =< aux(2) with precondition: [Out=0,V1>=0,V>=0] * Chain [32]: 2 with precondition: [V=0,Out=0,V1>=1] #### Cost of chains of quot(V1,V,Out): * Chain [[36],37]: 6*it(36)+6*s(25)+1 Such that:aux(9) =< V1 it(36) =< aux(9) s(28) =< it(36)*aux(9) s(25) =< s(28) with precondition: [V=1,Out>=1,V1>=Out+1] * Chain [[36],35,37]: 8*it(36)+6*s(25)+2*s(32)+5 Such that:s(30) =< 1 aux(10) =< V1 it(36) =< aux(10) s(32) =< s(30) s(28) =< it(36)*aux(10) s(25) =< s(28) with precondition: [V=1,Out>=2,V1>=Out] * Chain [[34],37]: 4*it(34)+3*s(45)+4*s(46)+1*s(48)+1 Such that:aux(13) =< V1 aux(12) =< V1+1 aux(11) =< V1-V it(34) =< V1/2-V/2 s(41) =< V s(49) =< aux(12) s(49) =< aux(13) s(45) =< it(34)*aux(11) s(46) =< s(49) s(48) =< s(45)*s(41) with precondition: [V>=2,Out>=1,V1+1>=2*Out+V] * Chain [[34],35,37]: 6*it(34)+2*s(32)+3*s(45)+4*s(46)+1*s(48)+5 Such that:aux(12) =< V1+1 aux(11) =< V1-V aux(14) =< V1 aux(15) =< V it(34) =< aux(14) s(32) =< aux(15) s(49) =< aux(12) s(49) =< aux(14) s(45) =< it(34)*aux(11) s(46) =< s(49) s(48) =< s(45)*aux(15) with precondition: [V>=2,Out>=2,V1+3>=2*Out+V] * Chain [37]: 1 with precondition: [Out=0,V1>=0,V>=0] * Chain [35,37]: 2*s(31)+2*s(32)+5 Such that:s(29) =< V1 s(30) =< V s(31) =< s(29) s(32) =< s(30) with precondition: [Out=1,V1>=1,V>=1] #### Cost of chains of encArg(V1,Out): * Chain [53]: 0 with precondition: [V1=1,Out=1] * Chain [52]: 0 with precondition: [V1=2,Out=2] * Chain [51]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([38,39,40,41,42,43,44,45,46,47,48,49,50],[[53],[52],[51]])]: 4*it(38)+4*it(39)+4*it(40)+1*it(41)+5*it(43)+8*it(44)+6*it(46)+1*it(47)+3*it(49)+3*it(50)+7*s(154)+1*s(155)+8*s(157)+2*s(159)+2*s(160)+12*s(163)+3*s(164)+1*s(165)+23*s(167)+2*s(168)+6*s(169)+4*s(174)+6*s(175)+6*s(176)+1*s(177)+1*s(181)+3*s(182)+2*s(183)+8*s(186)+1*s(188)+2*s(189)+2*s(190)+0 Such that:s(119) =< 2*V1 it([53]) =< 2/3*V1+1/3 aux(49) =< V1 aux(50) =< 2*V1+1 aux(51) =< V1/2 aux(52) =< 2/3*V1 aux(53) =< 3/5*V1 aux(54) =< 3/8*V1 aux(55) =< 4/5*V1 aux(56) =< 4/7*V1 aux(57) =< 4/9*V1 it(41) =< aux(49) it(43) =< aux(49) it(44) =< aux(49) it(46) =< aux(49) it(47) =< aux(49) it(49) =< aux(49) it(50) =< aux(49) it([53]) =< aux(49) it([51]) =< aux(50) it([53]) =< aux(50) it(39) =< aux(51) it(46) =< aux(52) it(40) =< aux(53) it(38) =< aux(54) it(49) =< aux(55) aux(34) =< aux(56) it(44) =< aux(56) it(43) =< aux(57) aux(25) =< s(119)+1 aux(45) =< s(119)+3 aux(27) =< s(119) aux(35) =< s(119)+2 aux(30) =< s(119)-1 it(49) =< it([51])*(1/5)+aux(55) it(50) =< it([51])*(1/5)+aux(55) it(46) =< it([51])*(1/3)+aux(52) it(47) =< it([51])*(1/3)+aux(52) it(49) =< it([51])*(1/3)+aux(52) it(50) =< it([51])*(1/3)+aux(52) it(44) =< it([51])*(3/7)+aux(56) it(46) =< it([51])*(3/7)+aux(56) it(47) =< it([51])*(3/7)+aux(56) it(49) =< it([51])*(3/7)+aux(56) it(50) =< it([51])*(3/7)+aux(56) aux(34) =< it([51])*(3/7)+aux(56) it(43) =< it([51])*(5/9)+it([53])*(1/9)+aux(57) it(44) =< it([51])*(5/9)+it([53])*(1/9)+aux(57) it(46) =< it([51])*(5/9)+it([53])*(1/9)+aux(57) it(47) =< it([51])*(5/9)+it([53])*(1/9)+aux(57) it(49) =< it([51])*(5/9)+it([53])*(1/9)+aux(57) it(50) =< it([51])*(5/9)+it([53])*(1/9)+aux(57) it(40) =< it([51])*(1/5)+aux(53) it(41) =< it([51])*(1/5)+aux(53) it(39) =< it([51])*(1/4)+aux(51) it(40) =< it([51])*(1/4)+aux(51) it(41) =< it([51])*(1/4)+aux(51) it(38) =< it([51])*(5/16)+aux(54) it(39) =< it([51])*(5/16)+aux(54) it(40) =< it([51])*(5/16)+aux(54) it(41) =< it([51])*(5/16)+aux(54) s(188) =< it(50)*aux(25) s(192) =< it(50)*aux(25) s(191) =< it(50)*aux(45) s(187) =< it(49)*aux(45) s(185) =< it(46)*aux(27) s(184) =< it(46)*aux(35) s(181) =< it(46)*aux(27) s(179) =< it(44)*aux(27) s(172) =< it(44)*aux(35) s(166) =< it(43)*aux(25) s(161) =< it(40)*aux(30) s(162) =< it(40)*aux(27) s(158) =< it(39)*aux(27) s(156) =< it(38)*aux(25) s(189) =< s(192) s(190) =< s(191) s(186) =< s(187) s(182) =< s(185) s(183) =< s(184) s(167) =< s(172) s(174) =< s(167)*aux(35) s(177) =< s(174)*aux(35) s(175) =< s(179) s(178) =< s(175)*s(119) s(176) =< s(178) s(168) =< aux(34) s(170) =< s(167)*aux(35) s(169) =< s(170) s(163) =< s(166) s(164) =< s(163)*aux(25) s(165) =< s(164)*aux(25) s(159) =< s(162) s(160) =< s(161) s(157) =< s(158) s(154) =< s(156) s(155) =< s(154)*aux(25) with precondition: [V1>=1,Out>=0,2*V1>=Out] #### Cost of chains of fun(V1,V,Out): * Chain [59]: 2*s(268)+10*s(269)+16*s(270)+12*s(271)+2*s(272)+6*s(273)+6*s(274)+8*s(275)+8*s(276)+8*s(277)+2*s(284)+2*s(290)+4*s(298)+4*s(299)+16*s(300)+6*s(301)+4*s(302)+46*s(303)+8*s(304)+2*s(305)+12*s(306)+12*s(308)+4*s(309)+12*s(311)+24*s(312)+6*s(313)+2*s(314)+4*s(315)+4*s(316)+16*s(317)+14*s(318)+2*s(319)+3*s(331)+15*s(332)+24*s(333)+18*s(334)+3*s(335)+9*s(336)+9*s(337)+12*s(338)+12*s(339)+12*s(340)+3*s(347)+3*s(353)+6*s(361)+6*s(362)+24*s(363)+9*s(364)+6*s(365)+69*s(366)+12*s(367)+3*s(368)+18*s(369)+18*s(371)+6*s(372)+18*s(374)+36*s(375)+9*s(376)+3*s(377)+6*s(378)+6*s(379)+24*s(380)+21*s(381)+3*s(382)+3*s(383)+1*s(512)+0 Such that:s(512) =< 2 aux(61) =< V1 aux(62) =< 2*V1 aux(63) =< 2*V1+1 aux(64) =< V1/2 aux(65) =< 2/3*V1 aux(66) =< 2/3*V1+1/3 aux(67) =< 3/5*V1 aux(68) =< 3/8*V1 aux(69) =< 4/5*V1 aux(70) =< 4/7*V1 aux(71) =< 4/9*V1 aux(72) =< V aux(73) =< 2*V aux(74) =< 2*V+1 aux(75) =< V/2 aux(76) =< 2/3*V aux(77) =< 2/3*V+1/3 aux(78) =< 3/5*V aux(79) =< 3/8*V aux(80) =< 4/5*V aux(81) =< 4/7*V aux(82) =< 4/9*V s(262) =< aux(66) s(325) =< aux(77) s(383) =< aux(73) s(331) =< aux(72) s(332) =< aux(72) s(333) =< aux(72) s(334) =< aux(72) s(335) =< aux(72) s(336) =< aux(72) s(337) =< aux(72) s(325) =< aux(72) s(325) =< aux(74) s(338) =< aux(75) s(334) =< aux(76) s(339) =< aux(78) s(340) =< aux(79) s(336) =< aux(80) s(341) =< aux(81) s(333) =< aux(81) s(332) =< aux(82) s(342) =< aux(73)+1 s(343) =< aux(73)+3 s(344) =< aux(73) s(345) =< aux(73)+2 s(346) =< aux(73)-1 s(336) =< aux(74)*(1/5)+aux(80) s(337) =< aux(74)*(1/5)+aux(80) s(334) =< aux(74)*(1/3)+aux(76) s(335) =< aux(74)*(1/3)+aux(76) s(336) =< aux(74)*(1/3)+aux(76) s(337) =< aux(74)*(1/3)+aux(76) s(333) =< aux(74)*(3/7)+aux(81) s(334) =< aux(74)*(3/7)+aux(81) s(335) =< aux(74)*(3/7)+aux(81) s(336) =< aux(74)*(3/7)+aux(81) s(337) =< aux(74)*(3/7)+aux(81) s(341) =< aux(74)*(3/7)+aux(81) s(332) =< aux(74)*(5/9)+s(325)*(1/9)+aux(82) s(333) =< aux(74)*(5/9)+s(325)*(1/9)+aux(82) s(334) =< aux(74)*(5/9)+s(325)*(1/9)+aux(82) s(335) =< aux(74)*(5/9)+s(325)*(1/9)+aux(82) s(336) =< aux(74)*(5/9)+s(325)*(1/9)+aux(82) s(337) =< aux(74)*(5/9)+s(325)*(1/9)+aux(82) s(339) =< aux(74)*(1/5)+aux(78) s(331) =< aux(74)*(1/5)+aux(78) s(338) =< aux(74)*(1/4)+aux(75) s(339) =< aux(74)*(1/4)+aux(75) s(331) =< aux(74)*(1/4)+aux(75) s(340) =< aux(74)*(5/16)+aux(79) s(338) =< aux(74)*(5/16)+aux(79) s(339) =< aux(74)*(5/16)+aux(79) s(331) =< aux(74)*(5/16)+aux(79) s(347) =< s(337)*s(342) s(348) =< s(337)*s(342) s(349) =< s(337)*s(343) s(350) =< s(336)*s(343) s(351) =< s(334)*s(344) s(352) =< s(334)*s(345) s(353) =< s(334)*s(344) s(354) =< s(333)*s(344) s(355) =< s(333)*s(345) s(356) =< s(332)*s(342) s(357) =< s(339)*s(346) s(358) =< s(339)*s(344) s(359) =< s(338)*s(344) s(360) =< s(340)*s(342) s(361) =< s(348) s(362) =< s(349) s(363) =< s(350) s(364) =< s(351) s(365) =< s(352) s(366) =< s(355) s(367) =< s(366)*s(345) s(368) =< s(367)*s(345) s(369) =< s(354) s(370) =< s(369)*aux(73) s(371) =< s(370) s(372) =< s(341) s(373) =< s(366)*s(345) s(374) =< s(373) s(375) =< s(356) s(376) =< s(375)*s(342) s(377) =< s(376)*s(342) s(378) =< s(358) s(379) =< s(357) s(380) =< s(359) s(381) =< s(360) s(382) =< s(381)*s(342) s(268) =< aux(61) s(269) =< aux(61) s(270) =< aux(61) s(271) =< aux(61) s(272) =< aux(61) s(273) =< aux(61) s(274) =< aux(61) s(262) =< aux(61) s(262) =< aux(63) s(275) =< aux(64) s(271) =< aux(65) s(276) =< aux(67) s(277) =< aux(68) s(273) =< aux(69) s(278) =< aux(70) s(270) =< aux(70) s(269) =< aux(71) s(279) =< aux(62)+1 s(280) =< aux(62)+3 s(281) =< aux(62) s(282) =< aux(62)+2 s(283) =< aux(62)-1 s(273) =< aux(63)*(1/5)+aux(69) s(274) =< aux(63)*(1/5)+aux(69) s(271) =< aux(63)*(1/3)+aux(65) s(272) =< aux(63)*(1/3)+aux(65) s(273) =< aux(63)*(1/3)+aux(65) s(274) =< aux(63)*(1/3)+aux(65) s(270) =< aux(63)*(3/7)+aux(70) s(271) =< aux(63)*(3/7)+aux(70) s(272) =< aux(63)*(3/7)+aux(70) s(273) =< aux(63)*(3/7)+aux(70) s(274) =< aux(63)*(3/7)+aux(70) s(278) =< aux(63)*(3/7)+aux(70) s(269) =< aux(63)*(5/9)+s(262)*(1/9)+aux(71) s(270) =< aux(63)*(5/9)+s(262)*(1/9)+aux(71) s(271) =< aux(63)*(5/9)+s(262)*(1/9)+aux(71) s(272) =< aux(63)*(5/9)+s(262)*(1/9)+aux(71) s(273) =< aux(63)*(5/9)+s(262)*(1/9)+aux(71) s(274) =< aux(63)*(5/9)+s(262)*(1/9)+aux(71) s(276) =< aux(63)*(1/5)+aux(67) s(268) =< aux(63)*(1/5)+aux(67) s(275) =< aux(63)*(1/4)+aux(64) s(276) =< aux(63)*(1/4)+aux(64) s(268) =< aux(63)*(1/4)+aux(64) s(277) =< aux(63)*(5/16)+aux(68) s(275) =< aux(63)*(5/16)+aux(68) s(276) =< aux(63)*(5/16)+aux(68) s(268) =< aux(63)*(5/16)+aux(68) s(284) =< s(274)*s(279) s(285) =< s(274)*s(279) s(286) =< s(274)*s(280) s(287) =< s(273)*s(280) s(288) =< s(271)*s(281) s(289) =< s(271)*s(282) s(290) =< s(271)*s(281) s(291) =< s(270)*s(281) s(292) =< s(270)*s(282) s(293) =< s(269)*s(279) s(294) =< s(276)*s(283) s(295) =< s(276)*s(281) s(296) =< s(275)*s(281) s(297) =< s(277)*s(279) s(298) =< s(285) s(299) =< s(286) s(300) =< s(287) s(301) =< s(288) s(302) =< s(289) s(303) =< s(292) s(304) =< s(303)*s(282) s(305) =< s(304)*s(282) s(306) =< s(291) s(307) =< s(306)*aux(62) s(308) =< s(307) s(309) =< s(278) s(310) =< s(303)*s(282) s(311) =< s(310) s(312) =< s(293) s(313) =< s(312)*s(279) s(314) =< s(313)*s(279) s(315) =< s(295) s(316) =< s(294) s(317) =< s(296) s(318) =< s(297) s(319) =< s(318)*s(279) with precondition: [Out=0,V1>=0,V>=0] * Chain [58]: 3*s(590)+15*s(591)+24*s(592)+18*s(593)+3*s(594)+9*s(595)+9*s(596)+12*s(597)+12*s(598)+12*s(599)+3*s(606)+3*s(612)+6*s(620)+6*s(621)+24*s(622)+9*s(623)+6*s(624)+69*s(625)+12*s(626)+3*s(627)+18*s(628)+18*s(630)+6*s(631)+18*s(633)+36*s(634)+9*s(635)+3*s(636)+6*s(637)+6*s(638)+24*s(639)+21*s(640)+3*s(641)+4*s(653)+20*s(654)+32*s(655)+24*s(656)+4*s(657)+12*s(658)+12*s(659)+16*s(660)+16*s(661)+16*s(662)+4*s(669)+4*s(675)+8*s(683)+8*s(684)+32*s(685)+12*s(686)+8*s(687)+92*s(688)+16*s(689)+4*s(690)+24*s(691)+24*s(693)+8*s(694)+24*s(696)+48*s(697)+12*s(698)+4*s(699)+8*s(700)+8*s(701)+32*s(702)+28*s(703)+4*s(704)+1*s(831)+2*s(958)+1 Such that:aux(84) =< 2 aux(85) =< V1 aux(86) =< 2*V1 aux(87) =< 2*V1+1 aux(88) =< V1/2 aux(89) =< 2/3*V1 aux(90) =< 2/3*V1+1/3 aux(91) =< 3/5*V1 aux(92) =< 3/8*V1 aux(93) =< 4/5*V1 aux(94) =< 4/7*V1 aux(95) =< 4/9*V1 aux(96) =< V aux(97) =< 2*V aux(98) =< 2*V+1 aux(99) =< V/2 aux(100) =< 2/3*V aux(101) =< 2/3*V+1/3 aux(102) =< 3/5*V aux(103) =< 3/8*V aux(104) =< 4/5*V aux(105) =< 4/7*V aux(106) =< 4/9*V s(958) =< aux(84) s(584) =< aux(90) s(647) =< aux(101) s(653) =< aux(96) s(654) =< aux(96) s(655) =< aux(96) s(656) =< aux(96) s(657) =< aux(96) s(658) =< aux(96) s(659) =< aux(96) s(647) =< aux(96) s(647) =< aux(98) s(660) =< aux(99) s(656) =< aux(100) s(661) =< aux(102) s(662) =< aux(103) s(658) =< aux(104) s(663) =< aux(105) s(655) =< aux(105) s(654) =< aux(106) s(664) =< aux(97)+1 s(665) =< aux(97)+3 s(666) =< aux(97) s(667) =< aux(97)+2 s(668) =< aux(97)-1 s(658) =< aux(98)*(1/5)+aux(104) s(659) =< aux(98)*(1/5)+aux(104) s(656) =< aux(98)*(1/3)+aux(100) s(657) =< aux(98)*(1/3)+aux(100) s(658) =< aux(98)*(1/3)+aux(100) s(659) =< aux(98)*(1/3)+aux(100) s(655) =< aux(98)*(3/7)+aux(105) s(656) =< aux(98)*(3/7)+aux(105) s(657) =< aux(98)*(3/7)+aux(105) s(658) =< aux(98)*(3/7)+aux(105) s(659) =< aux(98)*(3/7)+aux(105) s(663) =< aux(98)*(3/7)+aux(105) s(654) =< aux(98)*(5/9)+s(647)*(1/9)+aux(106) s(655) =< aux(98)*(5/9)+s(647)*(1/9)+aux(106) s(656) =< aux(98)*(5/9)+s(647)*(1/9)+aux(106) s(657) =< aux(98)*(5/9)+s(647)*(1/9)+aux(106) s(658) =< aux(98)*(5/9)+s(647)*(1/9)+aux(106) s(659) =< aux(98)*(5/9)+s(647)*(1/9)+aux(106) s(661) =< aux(98)*(1/5)+aux(102) s(653) =< aux(98)*(1/5)+aux(102) s(660) =< aux(98)*(1/4)+aux(99) s(661) =< aux(98)*(1/4)+aux(99) s(653) =< aux(98)*(1/4)+aux(99) s(662) =< aux(98)*(5/16)+aux(103) s(660) =< aux(98)*(5/16)+aux(103) s(661) =< aux(98)*(5/16)+aux(103) s(653) =< aux(98)*(5/16)+aux(103) s(669) =< s(659)*s(664) s(670) =< s(659)*s(664) s(671) =< s(659)*s(665) s(672) =< s(658)*s(665) s(673) =< s(656)*s(666) s(674) =< s(656)*s(667) s(675) =< s(656)*s(666) s(676) =< s(655)*s(666) s(677) =< s(655)*s(667) s(678) =< s(654)*s(664) s(679) =< s(661)*s(668) s(680) =< s(661)*s(666) s(681) =< s(660)*s(666) s(682) =< s(662)*s(664) s(683) =< s(670) s(684) =< s(671) s(685) =< s(672) s(686) =< s(673) s(687) =< s(674) s(688) =< s(677) s(689) =< s(688)*s(667) s(690) =< s(689)*s(667) s(691) =< s(676) s(692) =< s(691)*aux(97) s(693) =< s(692) s(694) =< s(663) s(695) =< s(688)*s(667) s(696) =< s(695) s(697) =< s(678) s(698) =< s(697)*s(664) s(699) =< s(698)*s(664) s(700) =< s(680) s(701) =< s(679) s(702) =< s(681) s(703) =< s(682) s(704) =< s(703)*s(664) s(590) =< aux(85) s(591) =< aux(85) s(592) =< aux(85) s(593) =< aux(85) s(594) =< aux(85) s(595) =< aux(85) s(596) =< aux(85) s(584) =< aux(85) s(584) =< aux(87) s(597) =< aux(88) s(593) =< aux(89) s(598) =< aux(91) s(599) =< aux(92) s(595) =< aux(93) s(600) =< aux(94) s(592) =< aux(94) s(591) =< aux(95) s(601) =< aux(86)+1 s(602) =< aux(86)+3 s(603) =< aux(86) s(604) =< aux(86)+2 s(605) =< aux(86)-1 s(595) =< aux(87)*(1/5)+aux(93) s(596) =< aux(87)*(1/5)+aux(93) s(593) =< aux(87)*(1/3)+aux(89) s(594) =< aux(87)*(1/3)+aux(89) s(595) =< aux(87)*(1/3)+aux(89) s(596) =< aux(87)*(1/3)+aux(89) s(592) =< aux(87)*(3/7)+aux(94) s(593) =< aux(87)*(3/7)+aux(94) s(594) =< aux(87)*(3/7)+aux(94) s(595) =< aux(87)*(3/7)+aux(94) s(596) =< aux(87)*(3/7)+aux(94) s(600) =< aux(87)*(3/7)+aux(94) s(591) =< aux(87)*(5/9)+s(584)*(1/9)+aux(95) s(592) =< aux(87)*(5/9)+s(584)*(1/9)+aux(95) s(593) =< aux(87)*(5/9)+s(584)*(1/9)+aux(95) s(594) =< aux(87)*(5/9)+s(584)*(1/9)+aux(95) s(595) =< aux(87)*(5/9)+s(584)*(1/9)+aux(95) s(596) =< aux(87)*(5/9)+s(584)*(1/9)+aux(95) s(598) =< aux(87)*(1/5)+aux(91) s(590) =< aux(87)*(1/5)+aux(91) s(597) =< aux(87)*(1/4)+aux(88) s(598) =< aux(87)*(1/4)+aux(88) s(590) =< aux(87)*(1/4)+aux(88) s(599) =< aux(87)*(5/16)+aux(92) s(597) =< aux(87)*(5/16)+aux(92) s(598) =< aux(87)*(5/16)+aux(92) s(590) =< aux(87)*(5/16)+aux(92) s(606) =< s(596)*s(601) s(607) =< s(596)*s(601) s(608) =< s(596)*s(602) s(609) =< s(595)*s(602) s(610) =< s(593)*s(603) s(611) =< s(593)*s(604) s(612) =< s(593)*s(603) s(613) =< s(592)*s(603) s(614) =< s(592)*s(604) s(615) =< s(591)*s(601) s(616) =< s(598)*s(605) s(617) =< s(598)*s(603) s(618) =< s(597)*s(603) s(619) =< s(599)*s(601) s(620) =< s(607) s(621) =< s(608) s(622) =< s(609) s(623) =< s(610) s(624) =< s(611) s(625) =< s(614) s(626) =< s(625)*s(604) s(627) =< s(626)*s(604) s(628) =< s(613) s(629) =< s(628)*aux(86) s(630) =< s(629) s(631) =< s(600) s(632) =< s(625)*s(604) s(633) =< s(632) s(634) =< s(615) s(635) =< s(634)*s(601) s(636) =< s(635)*s(601) s(637) =< s(617) s(638) =< s(616) s(639) =< s(618) s(640) =< s(619) s(641) =< s(640)*s(601) s(831) =< aux(97) with precondition: [Out=2,V1>=0,V>=0] * Chain [57]: 3*s(1034)+15*s(1035)+24*s(1036)+18*s(1037)+3*s(1038)+9*s(1039)+9*s(1040)+12*s(1041)+12*s(1042)+12*s(1043)+3*s(1050)+3*s(1056)+6*s(1064)+6*s(1065)+24*s(1066)+9*s(1067)+6*s(1068)+69*s(1069)+12*s(1070)+3*s(1071)+18*s(1072)+18*s(1074)+6*s(1075)+18*s(1077)+36*s(1078)+9*s(1079)+3*s(1080)+6*s(1081)+6*s(1082)+24*s(1083)+21*s(1084)+3*s(1085)+4*s(1097)+20*s(1098)+32*s(1099)+24*s(1100)+4*s(1101)+12*s(1102)+12*s(1103)+16*s(1104)+16*s(1105)+16*s(1106)+4*s(1113)+4*s(1119)+8*s(1127)+8*s(1128)+32*s(1129)+12*s(1130)+8*s(1131)+92*s(1132)+16*s(1133)+4*s(1134)+24*s(1135)+24*s(1137)+8*s(1138)+24*s(1140)+48*s(1141)+12*s(1142)+4*s(1143)+8*s(1144)+8*s(1145)+32*s(1146)+28*s(1147)+4*s(1148)+1*s(1275)+1*s(1465)+1 Such that:s(1465) =< 1 aux(108) =< V1 aux(109) =< 2*V1 aux(110) =< 2*V1+1 aux(111) =< V1/2 aux(112) =< 2/3*V1 aux(113) =< 2/3*V1+1/3 aux(114) =< 3/5*V1 aux(115) =< 3/8*V1 aux(116) =< 4/5*V1 aux(117) =< 4/7*V1 aux(118) =< 4/9*V1 aux(119) =< V aux(120) =< 2*V aux(121) =< 2*V+1 aux(122) =< V/2 aux(123) =< 2/3*V aux(124) =< 2/3*V+1/3 aux(125) =< 3/5*V aux(126) =< 3/8*V aux(127) =< 4/5*V aux(128) =< 4/7*V aux(129) =< 4/9*V s(1028) =< aux(113) s(1091) =< aux(124) s(1097) =< aux(119) s(1098) =< aux(119) s(1099) =< aux(119) s(1100) =< aux(119) s(1101) =< aux(119) s(1102) =< aux(119) s(1103) =< aux(119) s(1091) =< aux(119) s(1091) =< aux(121) s(1104) =< aux(122) s(1100) =< aux(123) s(1105) =< aux(125) s(1106) =< aux(126) s(1102) =< aux(127) s(1107) =< aux(128) s(1099) =< aux(128) s(1098) =< aux(129) s(1108) =< aux(120)+1 s(1109) =< aux(120)+3 s(1110) =< aux(120) s(1111) =< aux(120)+2 s(1112) =< aux(120)-1 s(1102) =< aux(121)*(1/5)+aux(127) s(1103) =< aux(121)*(1/5)+aux(127) s(1100) =< aux(121)*(1/3)+aux(123) s(1101) =< aux(121)*(1/3)+aux(123) s(1102) =< aux(121)*(1/3)+aux(123) s(1103) =< aux(121)*(1/3)+aux(123) s(1099) =< aux(121)*(3/7)+aux(128) s(1100) =< aux(121)*(3/7)+aux(128) s(1101) =< aux(121)*(3/7)+aux(128) s(1102) =< aux(121)*(3/7)+aux(128) s(1103) =< aux(121)*(3/7)+aux(128) s(1107) =< aux(121)*(3/7)+aux(128) s(1098) =< aux(121)*(5/9)+s(1091)*(1/9)+aux(129) s(1099) =< aux(121)*(5/9)+s(1091)*(1/9)+aux(129) s(1100) =< aux(121)*(5/9)+s(1091)*(1/9)+aux(129) s(1101) =< aux(121)*(5/9)+s(1091)*(1/9)+aux(129) s(1102) =< aux(121)*(5/9)+s(1091)*(1/9)+aux(129) s(1103) =< aux(121)*(5/9)+s(1091)*(1/9)+aux(129) s(1105) =< aux(121)*(1/5)+aux(125) s(1097) =< aux(121)*(1/5)+aux(125) s(1104) =< aux(121)*(1/4)+aux(122) s(1105) =< aux(121)*(1/4)+aux(122) s(1097) =< aux(121)*(1/4)+aux(122) s(1106) =< aux(121)*(5/16)+aux(126) s(1104) =< aux(121)*(5/16)+aux(126) s(1105) =< aux(121)*(5/16)+aux(126) s(1097) =< aux(121)*(5/16)+aux(126) s(1113) =< s(1103)*s(1108) s(1114) =< s(1103)*s(1108) s(1115) =< s(1103)*s(1109) s(1116) =< s(1102)*s(1109) s(1117) =< s(1100)*s(1110) s(1118) =< s(1100)*s(1111) s(1119) =< s(1100)*s(1110) s(1120) =< s(1099)*s(1110) s(1121) =< s(1099)*s(1111) s(1122) =< s(1098)*s(1108) s(1123) =< s(1105)*s(1112) s(1124) =< s(1105)*s(1110) s(1125) =< s(1104)*s(1110) s(1126) =< s(1106)*s(1108) s(1127) =< s(1114) s(1128) =< s(1115) s(1129) =< s(1116) s(1130) =< s(1117) s(1131) =< s(1118) s(1132) =< s(1121) s(1133) =< s(1132)*s(1111) s(1134) =< s(1133)*s(1111) s(1135) =< s(1120) s(1136) =< s(1135)*aux(120) s(1137) =< s(1136) s(1138) =< s(1107) s(1139) =< s(1132)*s(1111) s(1140) =< s(1139) s(1141) =< s(1122) s(1142) =< s(1141)*s(1108) s(1143) =< s(1142)*s(1108) s(1144) =< s(1124) s(1145) =< s(1123) s(1146) =< s(1125) s(1147) =< s(1126) s(1148) =< s(1147)*s(1108) s(1034) =< aux(108) s(1035) =< aux(108) s(1036) =< aux(108) s(1037) =< aux(108) s(1038) =< aux(108) s(1039) =< aux(108) s(1040) =< aux(108) s(1028) =< aux(108) s(1028) =< aux(110) s(1041) =< aux(111) s(1037) =< aux(112) s(1042) =< aux(114) s(1043) =< aux(115) s(1039) =< aux(116) s(1044) =< aux(117) s(1036) =< aux(117) s(1035) =< aux(118) s(1045) =< aux(109)+1 s(1046) =< aux(109)+3 s(1047) =< aux(109) s(1048) =< aux(109)+2 s(1049) =< aux(109)-1 s(1039) =< aux(110)*(1/5)+aux(116) s(1040) =< aux(110)*(1/5)+aux(116) s(1037) =< aux(110)*(1/3)+aux(112) s(1038) =< aux(110)*(1/3)+aux(112) s(1039) =< aux(110)*(1/3)+aux(112) s(1040) =< aux(110)*(1/3)+aux(112) s(1036) =< aux(110)*(3/7)+aux(117) s(1037) =< aux(110)*(3/7)+aux(117) s(1038) =< aux(110)*(3/7)+aux(117) s(1039) =< aux(110)*(3/7)+aux(117) s(1040) =< aux(110)*(3/7)+aux(117) s(1044) =< aux(110)*(3/7)+aux(117) s(1035) =< aux(110)*(5/9)+s(1028)*(1/9)+aux(118) s(1036) =< aux(110)*(5/9)+s(1028)*(1/9)+aux(118) s(1037) =< aux(110)*(5/9)+s(1028)*(1/9)+aux(118) s(1038) =< aux(110)*(5/9)+s(1028)*(1/9)+aux(118) s(1039) =< aux(110)*(5/9)+s(1028)*(1/9)+aux(118) s(1040) =< aux(110)*(5/9)+s(1028)*(1/9)+aux(118) s(1042) =< aux(110)*(1/5)+aux(114) s(1034) =< aux(110)*(1/5)+aux(114) s(1041) =< aux(110)*(1/4)+aux(111) s(1042) =< aux(110)*(1/4)+aux(111) s(1034) =< aux(110)*(1/4)+aux(111) s(1043) =< aux(110)*(5/16)+aux(115) s(1041) =< aux(110)*(5/16)+aux(115) s(1042) =< aux(110)*(5/16)+aux(115) s(1034) =< aux(110)*(5/16)+aux(115) s(1050) =< s(1040)*s(1045) s(1051) =< s(1040)*s(1045) s(1052) =< s(1040)*s(1046) s(1053) =< s(1039)*s(1046) s(1054) =< s(1037)*s(1047) s(1055) =< s(1037)*s(1048) s(1056) =< s(1037)*s(1047) s(1057) =< s(1036)*s(1047) s(1058) =< s(1036)*s(1048) s(1059) =< s(1035)*s(1045) s(1060) =< s(1042)*s(1049) s(1061) =< s(1042)*s(1047) s(1062) =< s(1041)*s(1047) s(1063) =< s(1043)*s(1045) s(1064) =< s(1051) s(1065) =< s(1052) s(1066) =< s(1053) s(1067) =< s(1054) s(1068) =< s(1055) s(1069) =< s(1058) s(1070) =< s(1069)*s(1048) s(1071) =< s(1070)*s(1048) s(1072) =< s(1057) s(1073) =< s(1072)*aux(109) s(1074) =< s(1073) s(1075) =< s(1044) s(1076) =< s(1069)*s(1048) s(1077) =< s(1076) s(1078) =< s(1059) s(1079) =< s(1078)*s(1045) s(1080) =< s(1079)*s(1045) s(1081) =< s(1061) s(1082) =< s(1060) s(1083) =< s(1062) s(1084) =< s(1063) s(1085) =< s(1084)*s(1045) s(1275) =< aux(109) with precondition: [Out=1,V1>=1,V>=0] * Chain [56]: 1*s(1477)+5*s(1478)+8*s(1479)+6*s(1480)+1*s(1481)+3*s(1482)+3*s(1483)+4*s(1484)+4*s(1485)+4*s(1486)+1*s(1493)+1*s(1499)+2*s(1507)+2*s(1508)+8*s(1509)+3*s(1510)+2*s(1511)+23*s(1512)+4*s(1513)+1*s(1514)+6*s(1515)+6*s(1517)+2*s(1518)+6*s(1520)+12*s(1521)+3*s(1522)+1*s(1523)+2*s(1524)+2*s(1525)+8*s(1526)+7*s(1527)+1*s(1528)+2*s(1529)+0 Such that:s(1466) =< V1 s(1467) =< 2*V1 s(1468) =< 2*V1+1 s(1469) =< V1/2 s(1470) =< 2/3*V1 s(1471) =< 2/3*V1+1/3 s(1472) =< 3/5*V1 s(1473) =< 3/8*V1 s(1474) =< 4/5*V1 s(1475) =< 4/7*V1 s(1476) =< 4/9*V1 aux(130) =< 2 s(1529) =< aux(130) s(1477) =< s(1466) s(1478) =< s(1466) s(1479) =< s(1466) s(1480) =< s(1466) s(1481) =< s(1466) s(1482) =< s(1466) s(1483) =< s(1466) s(1471) =< s(1466) s(1471) =< s(1468) s(1484) =< s(1469) s(1480) =< s(1470) s(1485) =< s(1472) s(1486) =< s(1473) s(1482) =< s(1474) s(1487) =< s(1475) s(1479) =< s(1475) s(1478) =< s(1476) s(1488) =< s(1467)+1 s(1489) =< s(1467)+3 s(1490) =< s(1467) s(1491) =< s(1467)+2 s(1492) =< s(1467)-1 s(1482) =< s(1468)*(1/5)+s(1474) s(1483) =< s(1468)*(1/5)+s(1474) s(1480) =< s(1468)*(1/3)+s(1470) s(1481) =< s(1468)*(1/3)+s(1470) s(1482) =< s(1468)*(1/3)+s(1470) s(1483) =< s(1468)*(1/3)+s(1470) s(1479) =< s(1468)*(3/7)+s(1475) s(1480) =< s(1468)*(3/7)+s(1475) s(1481) =< s(1468)*(3/7)+s(1475) s(1482) =< s(1468)*(3/7)+s(1475) s(1483) =< s(1468)*(3/7)+s(1475) s(1487) =< s(1468)*(3/7)+s(1475) s(1478) =< s(1468)*(5/9)+s(1471)*(1/9)+s(1476) s(1479) =< s(1468)*(5/9)+s(1471)*(1/9)+s(1476) s(1480) =< s(1468)*(5/9)+s(1471)*(1/9)+s(1476) s(1481) =< s(1468)*(5/9)+s(1471)*(1/9)+s(1476) s(1482) =< s(1468)*(5/9)+s(1471)*(1/9)+s(1476) s(1483) =< s(1468)*(5/9)+s(1471)*(1/9)+s(1476) s(1485) =< s(1468)*(1/5)+s(1472) s(1477) =< s(1468)*(1/5)+s(1472) s(1484) =< s(1468)*(1/4)+s(1469) s(1485) =< s(1468)*(1/4)+s(1469) s(1477) =< s(1468)*(1/4)+s(1469) s(1486) =< s(1468)*(5/16)+s(1473) s(1484) =< s(1468)*(5/16)+s(1473) s(1485) =< s(1468)*(5/16)+s(1473) s(1477) =< s(1468)*(5/16)+s(1473) s(1493) =< s(1483)*s(1488) s(1494) =< s(1483)*s(1488) s(1495) =< s(1483)*s(1489) s(1496) =< s(1482)*s(1489) s(1497) =< s(1480)*s(1490) s(1498) =< s(1480)*s(1491) s(1499) =< s(1480)*s(1490) s(1500) =< s(1479)*s(1490) s(1501) =< s(1479)*s(1491) s(1502) =< s(1478)*s(1488) s(1503) =< s(1485)*s(1492) s(1504) =< s(1485)*s(1490) s(1505) =< s(1484)*s(1490) s(1506) =< s(1486)*s(1488) s(1507) =< s(1494) s(1508) =< s(1495) s(1509) =< s(1496) s(1510) =< s(1497) s(1511) =< s(1498) s(1512) =< s(1501) s(1513) =< s(1512)*s(1491) s(1514) =< s(1513)*s(1491) s(1515) =< s(1500) s(1516) =< s(1515)*s(1467) s(1517) =< s(1516) s(1518) =< s(1487) s(1519) =< s(1512)*s(1491) s(1520) =< s(1519) s(1521) =< s(1502) s(1522) =< s(1521)*s(1488) s(1523) =< s(1522)*s(1488) s(1524) =< s(1504) s(1525) =< s(1503) s(1526) =< s(1505) s(1527) =< s(1506) s(1528) =< s(1527)*s(1488) with precondition: [V=2,Out=0,V1>=0] * Chain [55]: 1*s(1542)+5*s(1543)+8*s(1544)+6*s(1545)+1*s(1546)+3*s(1547)+3*s(1548)+4*s(1549)+4*s(1550)+4*s(1551)+1*s(1558)+1*s(1564)+2*s(1572)+2*s(1573)+8*s(1574)+3*s(1575)+2*s(1576)+23*s(1577)+4*s(1578)+1*s(1579)+6*s(1580)+6*s(1582)+2*s(1583)+6*s(1585)+12*s(1586)+3*s(1587)+1*s(1588)+2*s(1589)+2*s(1590)+8*s(1591)+7*s(1592)+1*s(1593)+1*s(1594)+1 Such that:s(1594) =< 2 s(1531) =< V1 s(1532) =< 2*V1 s(1533) =< 2*V1+1 s(1534) =< V1/2 s(1535) =< 2/3*V1 s(1536) =< 2/3*V1+1/3 s(1537) =< 3/5*V1 s(1538) =< 3/8*V1 s(1539) =< 4/5*V1 s(1540) =< 4/7*V1 s(1541) =< 4/9*V1 s(1542) =< s(1531) s(1543) =< s(1531) s(1544) =< s(1531) s(1545) =< s(1531) s(1546) =< s(1531) s(1547) =< s(1531) s(1548) =< s(1531) s(1536) =< s(1531) s(1536) =< s(1533) s(1549) =< s(1534) s(1545) =< s(1535) s(1550) =< s(1537) s(1551) =< s(1538) s(1547) =< s(1539) s(1552) =< s(1540) s(1544) =< s(1540) s(1543) =< s(1541) s(1553) =< s(1532)+1 s(1554) =< s(1532)+3 s(1555) =< s(1532) s(1556) =< s(1532)+2 s(1557) =< s(1532)-1 s(1547) =< s(1533)*(1/5)+s(1539) s(1548) =< s(1533)*(1/5)+s(1539) s(1545) =< s(1533)*(1/3)+s(1535) s(1546) =< s(1533)*(1/3)+s(1535) s(1547) =< s(1533)*(1/3)+s(1535) s(1548) =< s(1533)*(1/3)+s(1535) s(1544) =< s(1533)*(3/7)+s(1540) s(1545) =< s(1533)*(3/7)+s(1540) s(1546) =< s(1533)*(3/7)+s(1540) s(1547) =< s(1533)*(3/7)+s(1540) s(1548) =< s(1533)*(3/7)+s(1540) s(1552) =< s(1533)*(3/7)+s(1540) s(1543) =< s(1533)*(5/9)+s(1536)*(1/9)+s(1541) s(1544) =< s(1533)*(5/9)+s(1536)*(1/9)+s(1541) s(1545) =< s(1533)*(5/9)+s(1536)*(1/9)+s(1541) s(1546) =< s(1533)*(5/9)+s(1536)*(1/9)+s(1541) s(1547) =< s(1533)*(5/9)+s(1536)*(1/9)+s(1541) s(1548) =< s(1533)*(5/9)+s(1536)*(1/9)+s(1541) s(1550) =< s(1533)*(1/5)+s(1537) s(1542) =< s(1533)*(1/5)+s(1537) s(1549) =< s(1533)*(1/4)+s(1534) s(1550) =< s(1533)*(1/4)+s(1534) s(1542) =< s(1533)*(1/4)+s(1534) s(1551) =< s(1533)*(5/16)+s(1538) s(1549) =< s(1533)*(5/16)+s(1538) s(1550) =< s(1533)*(5/16)+s(1538) s(1542) =< s(1533)*(5/16)+s(1538) s(1558) =< s(1548)*s(1553) s(1559) =< s(1548)*s(1553) s(1560) =< s(1548)*s(1554) s(1561) =< s(1547)*s(1554) s(1562) =< s(1545)*s(1555) s(1563) =< s(1545)*s(1556) s(1564) =< s(1545)*s(1555) s(1565) =< s(1544)*s(1555) s(1566) =< s(1544)*s(1556) s(1567) =< s(1543)*s(1553) s(1568) =< s(1550)*s(1557) s(1569) =< s(1550)*s(1555) s(1570) =< s(1549)*s(1555) s(1571) =< s(1551)*s(1553) s(1572) =< s(1559) s(1573) =< s(1560) s(1574) =< s(1561) s(1575) =< s(1562) s(1576) =< s(1563) s(1577) =< s(1566) s(1578) =< s(1577)*s(1556) s(1579) =< s(1578)*s(1556) s(1580) =< s(1565) s(1581) =< s(1580)*s(1532) s(1582) =< s(1581) s(1583) =< s(1552) s(1584) =< s(1577)*s(1556) s(1585) =< s(1584) s(1586) =< s(1567) s(1587) =< s(1586)*s(1553) s(1588) =< s(1587)*s(1553) s(1589) =< s(1569) s(1590) =< s(1568) s(1591) =< s(1570) s(1592) =< s(1571) s(1593) =< s(1592)*s(1553) with precondition: [V=2,Out=1,2*V1>=3] * Chain [54]: 2*s(1606)+10*s(1607)+16*s(1608)+12*s(1609)+2*s(1610)+6*s(1611)+6*s(1612)+8*s(1613)+8*s(1614)+8*s(1615)+2*s(1622)+2*s(1628)+4*s(1636)+4*s(1637)+16*s(1638)+6*s(1639)+4*s(1640)+46*s(1641)+8*s(1642)+2*s(1643)+12*s(1644)+12*s(1646)+4*s(1647)+12*s(1649)+24*s(1650)+6*s(1651)+2*s(1652)+4*s(1653)+4*s(1654)+16*s(1655)+14*s(1656)+2*s(1657)+1*s(1721)+1 Such that:s(1721) =< 2 aux(131) =< V1 aux(132) =< 2*V1 aux(133) =< 2*V1+1 aux(134) =< V1/2 aux(135) =< 2/3*V1 aux(136) =< 2/3*V1+1/3 aux(137) =< 3/5*V1 aux(138) =< 3/8*V1 aux(139) =< 4/5*V1 aux(140) =< 4/7*V1 aux(141) =< 4/9*V1 s(1600) =< aux(136) s(1606) =< aux(131) s(1607) =< aux(131) s(1608) =< aux(131) s(1609) =< aux(131) s(1610) =< aux(131) s(1611) =< aux(131) s(1612) =< aux(131) s(1600) =< aux(131) s(1600) =< aux(133) s(1613) =< aux(134) s(1609) =< aux(135) s(1614) =< aux(137) s(1615) =< aux(138) s(1611) =< aux(139) s(1616) =< aux(140) s(1608) =< aux(140) s(1607) =< aux(141) s(1617) =< aux(132)+1 s(1618) =< aux(132)+3 s(1619) =< aux(132) s(1620) =< aux(132)+2 s(1621) =< aux(132)-1 s(1611) =< aux(133)*(1/5)+aux(139) s(1612) =< aux(133)*(1/5)+aux(139) s(1609) =< aux(133)*(1/3)+aux(135) s(1610) =< aux(133)*(1/3)+aux(135) s(1611) =< aux(133)*(1/3)+aux(135) s(1612) =< aux(133)*(1/3)+aux(135) s(1608) =< aux(133)*(3/7)+aux(140) s(1609) =< aux(133)*(3/7)+aux(140) s(1610) =< aux(133)*(3/7)+aux(140) s(1611) =< aux(133)*(3/7)+aux(140) s(1612) =< aux(133)*(3/7)+aux(140) s(1616) =< aux(133)*(3/7)+aux(140) s(1607) =< aux(133)*(5/9)+s(1600)*(1/9)+aux(141) s(1608) =< aux(133)*(5/9)+s(1600)*(1/9)+aux(141) s(1609) =< aux(133)*(5/9)+s(1600)*(1/9)+aux(141) s(1610) =< aux(133)*(5/9)+s(1600)*(1/9)+aux(141) s(1611) =< aux(133)*(5/9)+s(1600)*(1/9)+aux(141) s(1612) =< aux(133)*(5/9)+s(1600)*(1/9)+aux(141) s(1614) =< aux(133)*(1/5)+aux(137) s(1606) =< aux(133)*(1/5)+aux(137) s(1613) =< aux(133)*(1/4)+aux(134) s(1614) =< aux(133)*(1/4)+aux(134) s(1606) =< aux(133)*(1/4)+aux(134) s(1615) =< aux(133)*(5/16)+aux(138) s(1613) =< aux(133)*(5/16)+aux(138) s(1614) =< aux(133)*(5/16)+aux(138) s(1606) =< aux(133)*(5/16)+aux(138) s(1622) =< s(1612)*s(1617) s(1623) =< s(1612)*s(1617) s(1624) =< s(1612)*s(1618) s(1625) =< s(1611)*s(1618) s(1626) =< s(1609)*s(1619) s(1627) =< s(1609)*s(1620) s(1628) =< s(1609)*s(1619) s(1629) =< s(1608)*s(1619) s(1630) =< s(1608)*s(1620) s(1631) =< s(1607)*s(1617) s(1632) =< s(1614)*s(1621) s(1633) =< s(1614)*s(1619) s(1634) =< s(1613)*s(1619) s(1635) =< s(1615)*s(1617) s(1636) =< s(1623) s(1637) =< s(1624) s(1638) =< s(1625) s(1639) =< s(1626) s(1640) =< s(1627) s(1641) =< s(1630) s(1642) =< s(1641)*s(1620) s(1643) =< s(1642)*s(1620) s(1644) =< s(1629) s(1645) =< s(1644)*aux(132) s(1646) =< s(1645) s(1647) =< s(1616) s(1648) =< s(1641)*s(1620) s(1649) =< s(1648) s(1650) =< s(1631) s(1651) =< s(1650)*s(1617) s(1652) =< s(1651)*s(1617) s(1653) =< s(1633) s(1654) =< s(1632) s(1655) =< s(1634) s(1656) =< s(1635) s(1657) =< s(1656)*s(1617) with precondition: [V=2,Out=2,V1>=0] #### Cost of chains of fun2(Out): * Chain [61]: 0 with precondition: [Out=0] * Chain [60]: 0 with precondition: [Out=2] #### Cost of chains of fun3(V1,Out): * Chain [64]: 1*s(2318)+5*s(2319)+8*s(2320)+6*s(2321)+1*s(2322)+3*s(2323)+3*s(2324)+4*s(2325)+4*s(2326)+4*s(2327)+1*s(2334)+1*s(2340)+2*s(2348)+2*s(2349)+8*s(2350)+3*s(2351)+2*s(2352)+23*s(2353)+4*s(2354)+1*s(2355)+6*s(2356)+6*s(2358)+2*s(2359)+6*s(2361)+12*s(2362)+3*s(2363)+1*s(2364)+2*s(2365)+2*s(2366)+8*s(2367)+7*s(2368)+1*s(2369)+0 Such that:s(2307) =< V1 s(2308) =< 2*V1 s(2309) =< 2*V1+1 s(2310) =< V1/2 s(2311) =< 2/3*V1 s(2312) =< 2/3*V1+1/3 s(2313) =< 3/5*V1 s(2314) =< 3/8*V1 s(2315) =< 4/5*V1 s(2316) =< 4/7*V1 s(2317) =< 4/9*V1 s(2318) =< s(2307) s(2319) =< s(2307) s(2320) =< s(2307) s(2321) =< s(2307) s(2322) =< s(2307) s(2323) =< s(2307) s(2324) =< s(2307) s(2312) =< s(2307) s(2312) =< s(2309) s(2325) =< s(2310) s(2321) =< s(2311) s(2326) =< s(2313) s(2327) =< s(2314) s(2323) =< s(2315) s(2328) =< s(2316) s(2320) =< s(2316) s(2319) =< s(2317) s(2329) =< s(2308)+1 s(2330) =< s(2308)+3 s(2331) =< s(2308) s(2332) =< s(2308)+2 s(2333) =< s(2308)-1 s(2323) =< s(2309)*(1/5)+s(2315) s(2324) =< s(2309)*(1/5)+s(2315) s(2321) =< s(2309)*(1/3)+s(2311) s(2322) =< s(2309)*(1/3)+s(2311) s(2323) =< s(2309)*(1/3)+s(2311) s(2324) =< s(2309)*(1/3)+s(2311) s(2320) =< s(2309)*(3/7)+s(2316) s(2321) =< s(2309)*(3/7)+s(2316) s(2322) =< s(2309)*(3/7)+s(2316) s(2323) =< s(2309)*(3/7)+s(2316) s(2324) =< s(2309)*(3/7)+s(2316) s(2328) =< s(2309)*(3/7)+s(2316) s(2319) =< s(2309)*(5/9)+s(2312)*(1/9)+s(2317) s(2320) =< s(2309)*(5/9)+s(2312)*(1/9)+s(2317) s(2321) =< s(2309)*(5/9)+s(2312)*(1/9)+s(2317) s(2322) =< s(2309)*(5/9)+s(2312)*(1/9)+s(2317) s(2323) =< s(2309)*(5/9)+s(2312)*(1/9)+s(2317) s(2324) =< s(2309)*(5/9)+s(2312)*(1/9)+s(2317) s(2326) =< s(2309)*(1/5)+s(2313) s(2318) =< s(2309)*(1/5)+s(2313) s(2325) =< s(2309)*(1/4)+s(2310) s(2326) =< s(2309)*(1/4)+s(2310) s(2318) =< s(2309)*(1/4)+s(2310) s(2327) =< s(2309)*(5/16)+s(2314) s(2325) =< s(2309)*(5/16)+s(2314) s(2326) =< s(2309)*(5/16)+s(2314) s(2318) =< s(2309)*(5/16)+s(2314) s(2334) =< s(2324)*s(2329) s(2335) =< s(2324)*s(2329) s(2336) =< s(2324)*s(2330) s(2337) =< s(2323)*s(2330) s(2338) =< s(2321)*s(2331) s(2339) =< s(2321)*s(2332) s(2340) =< s(2321)*s(2331) s(2341) =< s(2320)*s(2331) s(2342) =< s(2320)*s(2332) s(2343) =< s(2319)*s(2329) s(2344) =< s(2326)*s(2333) s(2345) =< s(2326)*s(2331) s(2346) =< s(2325)*s(2331) s(2347) =< s(2327)*s(2329) s(2348) =< s(2335) s(2349) =< s(2336) s(2350) =< s(2337) s(2351) =< s(2338) s(2352) =< s(2339) s(2353) =< s(2342) s(2354) =< s(2353)*s(2332) s(2355) =< s(2354)*s(2332) s(2356) =< s(2341) s(2357) =< s(2356)*s(2308) s(2358) =< s(2357) s(2359) =< s(2328) s(2360) =< s(2353)*s(2332) s(2361) =< s(2360) s(2362) =< s(2343) s(2363) =< s(2362)*s(2329) s(2364) =< s(2363)*s(2329) s(2365) =< s(2345) s(2366) =< s(2344) s(2367) =< s(2346) s(2368) =< s(2347) s(2369) =< s(2368)*s(2329) with precondition: [V1>=1,Out>=1,2*V1+1>=Out] * Chain [63]: 0 with precondition: [Out=0,V1>=0] * Chain [62]: 0 with precondition: [Out=1,V1>=0] #### Cost of chains of fun4(Out): * Chain [66]: 0 with precondition: [Out=0] * Chain [65]: 0 with precondition: [Out=1] #### Cost of chains of fun5(V1,V,Out): * Chain [70]: 2*s(2381)+10*s(2382)+16*s(2383)+12*s(2384)+2*s(2385)+6*s(2386)+6*s(2387)+8*s(2388)+8*s(2389)+8*s(2390)+2*s(2397)+2*s(2403)+4*s(2411)+4*s(2412)+16*s(2413)+6*s(2414)+4*s(2415)+46*s(2416)+8*s(2417)+2*s(2418)+12*s(2419)+12*s(2421)+4*s(2422)+12*s(2424)+24*s(2425)+6*s(2426)+2*s(2427)+4*s(2428)+4*s(2429)+16*s(2430)+14*s(2431)+2*s(2432)+3*s(2444)+15*s(2445)+24*s(2446)+18*s(2447)+3*s(2448)+9*s(2449)+9*s(2450)+12*s(2451)+12*s(2452)+12*s(2453)+3*s(2460)+3*s(2466)+6*s(2474)+6*s(2475)+24*s(2476)+9*s(2477)+6*s(2478)+69*s(2479)+12*s(2480)+3*s(2481)+18*s(2482)+18*s(2484)+6*s(2485)+18*s(2487)+36*s(2488)+9*s(2489)+3*s(2490)+6*s(2491)+6*s(2492)+24*s(2493)+21*s(2494)+3*s(2495)+4*s(2498)+6*s(2499)+8*s(2632)+3 Such that:aux(184) =< 2 aux(185) =< V1 aux(186) =< 2*V1 aux(187) =< 2*V1+1 aux(188) =< V1/2 aux(189) =< 2/3*V1 aux(190) =< 2/3*V1+1/3 aux(191) =< 3/5*V1 aux(192) =< 3/8*V1 aux(193) =< 4/5*V1 aux(194) =< 4/7*V1 aux(195) =< 4/9*V1 aux(196) =< V aux(197) =< 2*V aux(198) =< 2*V+1 aux(199) =< V/2 aux(200) =< 2/3*V aux(201) =< 2/3*V+1/3 aux(202) =< 3/5*V aux(203) =< 3/8*V aux(204) =< 4/5*V aux(205) =< 4/7*V aux(206) =< 4/9*V s(2375) =< aux(190) s(2438) =< aux(201) s(2632) =< aux(184) s(2499) =< aux(197) s(2444) =< aux(196) s(2445) =< aux(196) s(2446) =< aux(196) s(2447) =< aux(196) s(2448) =< aux(196) s(2449) =< aux(196) s(2450) =< aux(196) s(2438) =< aux(196) s(2438) =< aux(198) s(2451) =< aux(199) s(2447) =< aux(200) s(2452) =< aux(202) s(2453) =< aux(203) s(2449) =< aux(204) s(2454) =< aux(205) s(2446) =< aux(205) s(2445) =< aux(206) s(2455) =< aux(197)+1 s(2456) =< aux(197)+3 s(2457) =< aux(197) s(2458) =< aux(197)+2 s(2459) =< aux(197)-1 s(2449) =< aux(198)*(1/5)+aux(204) s(2450) =< aux(198)*(1/5)+aux(204) s(2447) =< aux(198)*(1/3)+aux(200) s(2448) =< aux(198)*(1/3)+aux(200) s(2449) =< aux(198)*(1/3)+aux(200) s(2450) =< aux(198)*(1/3)+aux(200) s(2446) =< aux(198)*(3/7)+aux(205) s(2447) =< aux(198)*(3/7)+aux(205) s(2448) =< aux(198)*(3/7)+aux(205) s(2449) =< aux(198)*(3/7)+aux(205) s(2450) =< aux(198)*(3/7)+aux(205) s(2454) =< aux(198)*(3/7)+aux(205) s(2445) =< aux(198)*(5/9)+s(2438)*(1/9)+aux(206) s(2446) =< aux(198)*(5/9)+s(2438)*(1/9)+aux(206) s(2447) =< aux(198)*(5/9)+s(2438)*(1/9)+aux(206) s(2448) =< aux(198)*(5/9)+s(2438)*(1/9)+aux(206) s(2449) =< aux(198)*(5/9)+s(2438)*(1/9)+aux(206) s(2450) =< aux(198)*(5/9)+s(2438)*(1/9)+aux(206) s(2452) =< aux(198)*(1/5)+aux(202) s(2444) =< aux(198)*(1/5)+aux(202) s(2451) =< aux(198)*(1/4)+aux(199) s(2452) =< aux(198)*(1/4)+aux(199) s(2444) =< aux(198)*(1/4)+aux(199) s(2453) =< aux(198)*(5/16)+aux(203) s(2451) =< aux(198)*(5/16)+aux(203) s(2452) =< aux(198)*(5/16)+aux(203) s(2444) =< aux(198)*(5/16)+aux(203) s(2460) =< s(2450)*s(2455) s(2461) =< s(2450)*s(2455) s(2462) =< s(2450)*s(2456) s(2463) =< s(2449)*s(2456) s(2464) =< s(2447)*s(2457) s(2465) =< s(2447)*s(2458) s(2466) =< s(2447)*s(2457) s(2467) =< s(2446)*s(2457) s(2468) =< s(2446)*s(2458) s(2469) =< s(2445)*s(2455) s(2470) =< s(2452)*s(2459) s(2471) =< s(2452)*s(2457) s(2472) =< s(2451)*s(2457) s(2473) =< s(2453)*s(2455) s(2474) =< s(2461) s(2475) =< s(2462) s(2476) =< s(2463) s(2477) =< s(2464) s(2478) =< s(2465) s(2479) =< s(2468) s(2480) =< s(2479)*s(2458) s(2481) =< s(2480)*s(2458) s(2482) =< s(2467) s(2483) =< s(2482)*aux(197) s(2484) =< s(2483) s(2485) =< s(2454) s(2486) =< s(2479)*s(2458) s(2487) =< s(2486) s(2488) =< s(2469) s(2489) =< s(2488)*s(2455) s(2490) =< s(2489)*s(2455) s(2491) =< s(2471) s(2492) =< s(2470) s(2493) =< s(2472) s(2494) =< s(2473) s(2495) =< s(2494)*s(2455) s(2498) =< aux(186) s(2381) =< aux(185) s(2382) =< aux(185) s(2383) =< aux(185) s(2384) =< aux(185) s(2385) =< aux(185) s(2386) =< aux(185) s(2387) =< aux(185) s(2375) =< aux(185) s(2375) =< aux(187) s(2388) =< aux(188) s(2384) =< aux(189) s(2389) =< aux(191) s(2390) =< aux(192) s(2386) =< aux(193) s(2391) =< aux(194) s(2383) =< aux(194) s(2382) =< aux(195) s(2392) =< aux(186)+1 s(2393) =< aux(186)+3 s(2394) =< aux(186) s(2395) =< aux(186)+2 s(2396) =< aux(186)-1 s(2386) =< aux(187)*(1/5)+aux(193) s(2387) =< aux(187)*(1/5)+aux(193) s(2384) =< aux(187)*(1/3)+aux(189) s(2385) =< aux(187)*(1/3)+aux(189) s(2386) =< aux(187)*(1/3)+aux(189) s(2387) =< aux(187)*(1/3)+aux(189) s(2383) =< aux(187)*(3/7)+aux(194) s(2384) =< aux(187)*(3/7)+aux(194) s(2385) =< aux(187)*(3/7)+aux(194) s(2386) =< aux(187)*(3/7)+aux(194) s(2387) =< aux(187)*(3/7)+aux(194) s(2391) =< aux(187)*(3/7)+aux(194) s(2382) =< aux(187)*(5/9)+s(2375)*(1/9)+aux(195) s(2383) =< aux(187)*(5/9)+s(2375)*(1/9)+aux(195) s(2384) =< aux(187)*(5/9)+s(2375)*(1/9)+aux(195) s(2385) =< aux(187)*(5/9)+s(2375)*(1/9)+aux(195) s(2386) =< aux(187)*(5/9)+s(2375)*(1/9)+aux(195) s(2387) =< aux(187)*(5/9)+s(2375)*(1/9)+aux(195) s(2389) =< aux(187)*(1/5)+aux(191) s(2381) =< aux(187)*(1/5)+aux(191) s(2388) =< aux(187)*(1/4)+aux(188) s(2389) =< aux(187)*(1/4)+aux(188) s(2381) =< aux(187)*(1/4)+aux(188) s(2390) =< aux(187)*(5/16)+aux(192) s(2388) =< aux(187)*(5/16)+aux(192) s(2389) =< aux(187)*(5/16)+aux(192) s(2381) =< aux(187)*(5/16)+aux(192) s(2397) =< s(2387)*s(2392) s(2398) =< s(2387)*s(2392) s(2399) =< s(2387)*s(2393) s(2400) =< s(2386)*s(2393) s(2401) =< s(2384)*s(2394) s(2402) =< s(2384)*s(2395) s(2403) =< s(2384)*s(2394) s(2404) =< s(2383)*s(2394) s(2405) =< s(2383)*s(2395) s(2406) =< s(2382)*s(2392) s(2407) =< s(2389)*s(2396) s(2408) =< s(2389)*s(2394) s(2409) =< s(2388)*s(2394) s(2410) =< s(2390)*s(2392) s(2411) =< s(2398) s(2412) =< s(2399) s(2413) =< s(2400) s(2414) =< s(2401) s(2415) =< s(2402) s(2416) =< s(2405) s(2417) =< s(2416)*s(2395) s(2418) =< s(2417)*s(2395) s(2419) =< s(2404) s(2420) =< s(2419)*aux(186) s(2421) =< s(2420) s(2422) =< s(2391) s(2423) =< s(2416)*s(2395) s(2424) =< s(2423) s(2425) =< s(2406) s(2426) =< s(2425)*s(2392) s(2427) =< s(2426)*s(2392) s(2428) =< s(2408) s(2429) =< s(2407) s(2430) =< s(2409) s(2431) =< s(2410) s(2432) =< s(2431)*s(2392) with precondition: [Out=0,V1>=0,V>=0] * Chain [69]: 3*s(2724)+15*s(2725)+24*s(2726)+18*s(2727)+3*s(2728)+9*s(2729)+9*s(2730)+12*s(2731)+12*s(2732)+12*s(2733)+3*s(2740)+3*s(2746)+6*s(2754)+6*s(2755)+24*s(2756)+9*s(2757)+6*s(2758)+69*s(2759)+12*s(2760)+3*s(2761)+18*s(2762)+18*s(2764)+6*s(2765)+18*s(2767)+36*s(2768)+9*s(2769)+3*s(2770)+6*s(2771)+6*s(2772)+24*s(2773)+21*s(2774)+3*s(2775)+4*s(2787)+20*s(2788)+32*s(2789)+24*s(2790)+4*s(2791)+12*s(2792)+12*s(2793)+16*s(2794)+16*s(2795)+16*s(2796)+4*s(2803)+4*s(2809)+8*s(2817)+8*s(2818)+32*s(2819)+12*s(2820)+8*s(2821)+92*s(2822)+16*s(2823)+4*s(2824)+24*s(2825)+24*s(2827)+8*s(2828)+24*s(2830)+48*s(2831)+12*s(2832)+4*s(2833)+8*s(2834)+8*s(2835)+32*s(2836)+28*s(2837)+4*s(2838)+23*s(2841)+1*s(2974)+12*s(3107)+11*s(3108)+1*s(3177)+3 Such that:aux(211) =< 1 aux(212) =< 2 aux(213) =< V1 aux(214) =< 2*V1 aux(215) =< 2*V1+1 aux(216) =< V1/2 aux(217) =< 2/3*V1 aux(218) =< 2/3*V1+1/3 aux(219) =< 3/5*V1 aux(220) =< 3/8*V1 aux(221) =< 4/5*V1 aux(222) =< 4/7*V1 aux(223) =< 4/9*V1 aux(224) =< V aux(225) =< 2*V aux(226) =< 2*V+1 aux(227) =< V/2 aux(228) =< 2/3*V aux(229) =< 2/3*V+1/3 aux(230) =< 3/5*V aux(231) =< 3/8*V aux(232) =< 4/5*V aux(233) =< 4/7*V aux(234) =< 4/9*V s(2718) =< aux(218) s(2781) =< aux(229) s(3107) =< aux(212) s(3108) =< aux(211) s(2787) =< aux(224) s(2788) =< aux(224) s(2789) =< aux(224) s(2790) =< aux(224) s(2791) =< aux(224) s(2792) =< aux(224) s(2793) =< aux(224) s(2781) =< aux(224) s(2781) =< aux(226) s(2794) =< aux(227) s(2790) =< aux(228) s(2795) =< aux(230) s(2796) =< aux(231) s(2792) =< aux(232) s(2797) =< aux(233) s(2789) =< aux(233) s(2788) =< aux(234) s(2798) =< aux(225)+1 s(2799) =< aux(225)+3 s(2800) =< aux(225) s(2801) =< aux(225)+2 s(2802) =< aux(225)-1 s(2792) =< aux(226)*(1/5)+aux(232) s(2793) =< aux(226)*(1/5)+aux(232) s(2790) =< aux(226)*(1/3)+aux(228) s(2791) =< aux(226)*(1/3)+aux(228) s(2792) =< aux(226)*(1/3)+aux(228) s(2793) =< aux(226)*(1/3)+aux(228) s(2789) =< aux(226)*(3/7)+aux(233) s(2790) =< aux(226)*(3/7)+aux(233) s(2791) =< aux(226)*(3/7)+aux(233) s(2792) =< aux(226)*(3/7)+aux(233) s(2793) =< aux(226)*(3/7)+aux(233) s(2797) =< aux(226)*(3/7)+aux(233) s(2788) =< aux(226)*(5/9)+s(2781)*(1/9)+aux(234) s(2789) =< aux(226)*(5/9)+s(2781)*(1/9)+aux(234) s(2790) =< aux(226)*(5/9)+s(2781)*(1/9)+aux(234) s(2791) =< aux(226)*(5/9)+s(2781)*(1/9)+aux(234) s(2792) =< aux(226)*(5/9)+s(2781)*(1/9)+aux(234) s(2793) =< aux(226)*(5/9)+s(2781)*(1/9)+aux(234) s(2795) =< aux(226)*(1/5)+aux(230) s(2787) =< aux(226)*(1/5)+aux(230) s(2794) =< aux(226)*(1/4)+aux(227) s(2795) =< aux(226)*(1/4)+aux(227) s(2787) =< aux(226)*(1/4)+aux(227) s(2796) =< aux(226)*(5/16)+aux(231) s(2794) =< aux(226)*(5/16)+aux(231) s(2795) =< aux(226)*(5/16)+aux(231) s(2787) =< aux(226)*(5/16)+aux(231) s(2803) =< s(2793)*s(2798) s(2804) =< s(2793)*s(2798) s(2805) =< s(2793)*s(2799) s(2806) =< s(2792)*s(2799) s(2807) =< s(2790)*s(2800) s(2808) =< s(2790)*s(2801) s(2809) =< s(2790)*s(2800) s(2810) =< s(2789)*s(2800) s(2811) =< s(2789)*s(2801) s(2812) =< s(2788)*s(2798) s(2813) =< s(2795)*s(2802) s(2814) =< s(2795)*s(2800) s(2815) =< s(2794)*s(2800) s(2816) =< s(2796)*s(2798) s(2817) =< s(2804) s(2818) =< s(2805) s(2819) =< s(2806) s(2820) =< s(2807) s(2821) =< s(2808) s(2822) =< s(2811) s(2823) =< s(2822)*s(2801) s(2824) =< s(2823)*s(2801) s(2825) =< s(2810) s(2826) =< s(2825)*aux(225) s(2827) =< s(2826) s(2828) =< s(2797) s(2829) =< s(2822)*s(2801) s(2830) =< s(2829) s(2831) =< s(2812) s(2832) =< s(2831)*s(2798) s(2833) =< s(2832)*s(2798) s(2834) =< s(2814) s(2835) =< s(2813) s(2836) =< s(2815) s(2837) =< s(2816) s(2838) =< s(2837)*s(2798) s(2841) =< aux(214) s(2724) =< aux(213) s(2725) =< aux(213) s(2726) =< aux(213) s(2727) =< aux(213) s(2728) =< aux(213) s(2729) =< aux(213) s(2730) =< aux(213) s(2718) =< aux(213) s(2718) =< aux(215) s(2731) =< aux(216) s(2727) =< aux(217) s(2732) =< aux(219) s(2733) =< aux(220) s(2729) =< aux(221) s(2734) =< aux(222) s(2726) =< aux(222) s(2725) =< aux(223) s(2735) =< aux(214)+1 s(2736) =< aux(214)+3 s(2737) =< aux(214) s(2738) =< aux(214)+2 s(2739) =< aux(214)-1 s(2729) =< aux(215)*(1/5)+aux(221) s(2730) =< aux(215)*(1/5)+aux(221) s(2727) =< aux(215)*(1/3)+aux(217) s(2728) =< aux(215)*(1/3)+aux(217) s(2729) =< aux(215)*(1/3)+aux(217) s(2730) =< aux(215)*(1/3)+aux(217) s(2726) =< aux(215)*(3/7)+aux(222) s(2727) =< aux(215)*(3/7)+aux(222) s(2728) =< aux(215)*(3/7)+aux(222) s(2729) =< aux(215)*(3/7)+aux(222) s(2730) =< aux(215)*(3/7)+aux(222) s(2734) =< aux(215)*(3/7)+aux(222) s(2725) =< aux(215)*(5/9)+s(2718)*(1/9)+aux(223) s(2726) =< aux(215)*(5/9)+s(2718)*(1/9)+aux(223) s(2727) =< aux(215)*(5/9)+s(2718)*(1/9)+aux(223) s(2728) =< aux(215)*(5/9)+s(2718)*(1/9)+aux(223) s(2729) =< aux(215)*(5/9)+s(2718)*(1/9)+aux(223) s(2730) =< aux(215)*(5/9)+s(2718)*(1/9)+aux(223) s(2732) =< aux(215)*(1/5)+aux(219) s(2724) =< aux(215)*(1/5)+aux(219) s(2731) =< aux(215)*(1/4)+aux(216) s(2732) =< aux(215)*(1/4)+aux(216) s(2724) =< aux(215)*(1/4)+aux(216) s(2733) =< aux(215)*(5/16)+aux(220) s(2731) =< aux(215)*(5/16)+aux(220) s(2732) =< aux(215)*(5/16)+aux(220) s(2724) =< aux(215)*(5/16)+aux(220) s(2740) =< s(2730)*s(2735) s(2741) =< s(2730)*s(2735) s(2742) =< s(2730)*s(2736) s(2743) =< s(2729)*s(2736) s(2744) =< s(2727)*s(2737) s(2745) =< s(2727)*s(2738) s(2746) =< s(2727)*s(2737) s(2747) =< s(2726)*s(2737) s(2748) =< s(2726)*s(2738) s(2749) =< s(2725)*s(2735) s(2750) =< s(2732)*s(2739) s(2751) =< s(2732)*s(2737) s(2752) =< s(2731)*s(2737) s(2753) =< s(2733)*s(2735) s(2754) =< s(2741) s(2755) =< s(2742) s(2756) =< s(2743) s(2757) =< s(2744) s(2758) =< s(2745) s(2759) =< s(2748) s(2760) =< s(2759)*s(2738) s(2761) =< s(2760)*s(2738) s(2762) =< s(2747) s(2763) =< s(2762)*aux(214) s(2764) =< s(2763) s(2765) =< s(2734) s(2766) =< s(2759)*s(2738) s(2767) =< s(2766) s(2768) =< s(2749) s(2769) =< s(2768)*s(2735) s(2770) =< s(2769)*s(2735) s(2771) =< s(2751) s(2772) =< s(2750) s(2773) =< s(2752) s(2774) =< s(2753) s(2775) =< s(2774)*s(2735) s(2974) =< s(2841)*aux(214) s(3177) =< s(3108)*aux(211) with precondition: [V1>=1,V>=0,Out>=1,2*V1>=Out] * Chain [68]: 1*s(3193)+5*s(3194)+8*s(3195)+6*s(3196)+1*s(3197)+3*s(3198)+3*s(3199)+4*s(3200)+4*s(3201)+4*s(3202)+1*s(3209)+1*s(3215)+2*s(3223)+2*s(3224)+8*s(3225)+3*s(3226)+2*s(3227)+23*s(3228)+4*s(3229)+1*s(3230)+6*s(3231)+6*s(3233)+2*s(3234)+6*s(3236)+12*s(3237)+3*s(3238)+1*s(3239)+2*s(3240)+2*s(3241)+8*s(3242)+7*s(3243)+1*s(3244)+2*s(3247)+4*s(3248)+3 Such that:s(3182) =< V1 aux(235) =< 2*V1 s(3184) =< 2*V1+1 s(3185) =< V1/2 s(3186) =< 2/3*V1 s(3187) =< 2/3*V1+1/3 s(3188) =< 3/5*V1 s(3189) =< 3/8*V1 s(3190) =< 4/5*V1 s(3191) =< 4/7*V1 s(3192) =< 4/9*V1 aux(236) =< 2 s(3247) =< aux(235) s(3248) =< aux(236) s(3193) =< s(3182) s(3194) =< s(3182) s(3195) =< s(3182) s(3196) =< s(3182) s(3197) =< s(3182) s(3198) =< s(3182) s(3199) =< s(3182) s(3187) =< s(3182) s(3187) =< s(3184) s(3200) =< s(3185) s(3196) =< s(3186) s(3201) =< s(3188) s(3202) =< s(3189) s(3198) =< s(3190) s(3203) =< s(3191) s(3195) =< s(3191) s(3194) =< s(3192) s(3204) =< aux(235)+1 s(3205) =< aux(235)+3 s(3206) =< aux(235) s(3207) =< aux(235)+2 s(3208) =< aux(235)-1 s(3198) =< s(3184)*(1/5)+s(3190) s(3199) =< s(3184)*(1/5)+s(3190) s(3196) =< s(3184)*(1/3)+s(3186) s(3197) =< s(3184)*(1/3)+s(3186) s(3198) =< s(3184)*(1/3)+s(3186) s(3199) =< s(3184)*(1/3)+s(3186) s(3195) =< s(3184)*(3/7)+s(3191) s(3196) =< s(3184)*(3/7)+s(3191) s(3197) =< s(3184)*(3/7)+s(3191) s(3198) =< s(3184)*(3/7)+s(3191) s(3199) =< s(3184)*(3/7)+s(3191) s(3203) =< s(3184)*(3/7)+s(3191) s(3194) =< s(3184)*(5/9)+s(3187)*(1/9)+s(3192) s(3195) =< s(3184)*(5/9)+s(3187)*(1/9)+s(3192) s(3196) =< s(3184)*(5/9)+s(3187)*(1/9)+s(3192) s(3197) =< s(3184)*(5/9)+s(3187)*(1/9)+s(3192) s(3198) =< s(3184)*(5/9)+s(3187)*(1/9)+s(3192) s(3199) =< s(3184)*(5/9)+s(3187)*(1/9)+s(3192) s(3201) =< s(3184)*(1/5)+s(3188) s(3193) =< s(3184)*(1/5)+s(3188) s(3200) =< s(3184)*(1/4)+s(3185) s(3201) =< s(3184)*(1/4)+s(3185) s(3193) =< s(3184)*(1/4)+s(3185) s(3202) =< s(3184)*(5/16)+s(3189) s(3200) =< s(3184)*(5/16)+s(3189) s(3201) =< s(3184)*(5/16)+s(3189) s(3193) =< s(3184)*(5/16)+s(3189) s(3209) =< s(3199)*s(3204) s(3210) =< s(3199)*s(3204) s(3211) =< s(3199)*s(3205) s(3212) =< s(3198)*s(3205) s(3213) =< s(3196)*s(3206) s(3214) =< s(3196)*s(3207) s(3215) =< s(3196)*s(3206) s(3216) =< s(3195)*s(3206) s(3217) =< s(3195)*s(3207) s(3218) =< s(3194)*s(3204) s(3219) =< s(3201)*s(3208) s(3220) =< s(3201)*s(3206) s(3221) =< s(3200)*s(3206) s(3222) =< s(3202)*s(3204) s(3223) =< s(3210) s(3224) =< s(3211) s(3225) =< s(3212) s(3226) =< s(3213) s(3227) =< s(3214) s(3228) =< s(3217) s(3229) =< s(3228)*s(3207) s(3230) =< s(3229)*s(3207) s(3231) =< s(3216) s(3232) =< s(3231)*aux(235) s(3233) =< s(3232) s(3234) =< s(3203) s(3235) =< s(3228)*s(3207) s(3236) =< s(3235) s(3237) =< s(3218) s(3238) =< s(3237)*s(3204) s(3239) =< s(3238)*s(3204) s(3240) =< s(3220) s(3241) =< s(3219) s(3242) =< s(3221) s(3243) =< s(3222) s(3244) =< s(3243)*s(3204) with precondition: [V=2,Out=0,V1>=0] * Chain [67]: 1*s(3264)+5*s(3265)+8*s(3266)+6*s(3267)+1*s(3268)+3*s(3269)+3*s(3270)+4*s(3271)+4*s(3272)+4*s(3273)+1*s(3280)+1*s(3286)+2*s(3294)+2*s(3295)+8*s(3296)+3*s(3297)+2*s(3298)+23*s(3299)+4*s(3300)+1*s(3301)+6*s(3302)+6*s(3304)+2*s(3305)+6*s(3307)+12*s(3308)+3*s(3309)+1*s(3310)+2*s(3311)+2*s(3312)+8*s(3313)+7*s(3314)+1*s(3315)+5*s(3317)+2*s(3320)+1*s(3321)+3 Such that:s(3318) =< 2 s(3253) =< V1 s(3255) =< 2*V1+1 s(3256) =< V1/2 s(3257) =< 2/3*V1 s(3258) =< 2/3*V1+1/3 s(3259) =< 3/5*V1 s(3260) =< 3/8*V1 s(3261) =< 4/5*V1 s(3262) =< 4/7*V1 s(3263) =< 4/9*V1 aux(237) =< 2*V1 s(3317) =< aux(237) s(3320) =< s(3318) s(3321) =< s(3317)*s(3318) s(3264) =< s(3253) s(3265) =< s(3253) s(3266) =< s(3253) s(3267) =< s(3253) s(3268) =< s(3253) s(3269) =< s(3253) s(3270) =< s(3253) s(3258) =< s(3253) s(3258) =< s(3255) s(3271) =< s(3256) s(3267) =< s(3257) s(3272) =< s(3259) s(3273) =< s(3260) s(3269) =< s(3261) s(3274) =< s(3262) s(3266) =< s(3262) s(3265) =< s(3263) s(3275) =< aux(237)+1 s(3276) =< aux(237)+3 s(3277) =< aux(237) s(3278) =< aux(237)+2 s(3279) =< aux(237)-1 s(3269) =< s(3255)*(1/5)+s(3261) s(3270) =< s(3255)*(1/5)+s(3261) s(3267) =< s(3255)*(1/3)+s(3257) s(3268) =< s(3255)*(1/3)+s(3257) s(3269) =< s(3255)*(1/3)+s(3257) s(3270) =< s(3255)*(1/3)+s(3257) s(3266) =< s(3255)*(3/7)+s(3262) s(3267) =< s(3255)*(3/7)+s(3262) s(3268) =< s(3255)*(3/7)+s(3262) s(3269) =< s(3255)*(3/7)+s(3262) s(3270) =< s(3255)*(3/7)+s(3262) s(3274) =< s(3255)*(3/7)+s(3262) s(3265) =< s(3255)*(5/9)+s(3258)*(1/9)+s(3263) s(3266) =< s(3255)*(5/9)+s(3258)*(1/9)+s(3263) s(3267) =< s(3255)*(5/9)+s(3258)*(1/9)+s(3263) s(3268) =< s(3255)*(5/9)+s(3258)*(1/9)+s(3263) s(3269) =< s(3255)*(5/9)+s(3258)*(1/9)+s(3263) s(3270) =< s(3255)*(5/9)+s(3258)*(1/9)+s(3263) s(3272) =< s(3255)*(1/5)+s(3259) s(3264) =< s(3255)*(1/5)+s(3259) s(3271) =< s(3255)*(1/4)+s(3256) s(3272) =< s(3255)*(1/4)+s(3256) s(3264) =< s(3255)*(1/4)+s(3256) s(3273) =< s(3255)*(5/16)+s(3260) s(3271) =< s(3255)*(5/16)+s(3260) s(3272) =< s(3255)*(5/16)+s(3260) s(3264) =< s(3255)*(5/16)+s(3260) s(3280) =< s(3270)*s(3275) s(3281) =< s(3270)*s(3275) s(3282) =< s(3270)*s(3276) s(3283) =< s(3269)*s(3276) s(3284) =< s(3267)*s(3277) s(3285) =< s(3267)*s(3278) s(3286) =< s(3267)*s(3277) s(3287) =< s(3266)*s(3277) s(3288) =< s(3266)*s(3278) s(3289) =< s(3265)*s(3275) s(3290) =< s(3272)*s(3279) s(3291) =< s(3272)*s(3277) s(3292) =< s(3271)*s(3277) s(3293) =< s(3273)*s(3275) s(3294) =< s(3281) s(3295) =< s(3282) s(3296) =< s(3283) s(3297) =< s(3284) s(3298) =< s(3285) s(3299) =< s(3288) s(3300) =< s(3299)*s(3278) s(3301) =< s(3300)*s(3278) s(3302) =< s(3287) s(3303) =< s(3302)*aux(237) s(3304) =< s(3303) s(3305) =< s(3274) s(3306) =< s(3299)*s(3278) s(3307) =< s(3306) s(3308) =< s(3289) s(3309) =< s(3308)*s(3275) s(3310) =< s(3309)*s(3275) s(3311) =< s(3291) s(3312) =< s(3290) s(3313) =< s(3292) s(3314) =< s(3293) s(3315) =< s(3314)*s(3275) with precondition: [V=2,Out>=1,2*V1>=Out+2] #### Cost of chains of fun6(V1,V,V2,Out): * Chain [77]: 6*s(3733)+30*s(3734)+48*s(3735)+36*s(3736)+6*s(3737)+18*s(3738)+18*s(3739)+24*s(3740)+24*s(3741)+24*s(3742)+6*s(3749)+6*s(3755)+12*s(3763)+12*s(3764)+48*s(3765)+18*s(3766)+12*s(3767)+138*s(3768)+24*s(3769)+6*s(3770)+36*s(3771)+36*s(3773)+12*s(3774)+36*s(3776)+72*s(3777)+18*s(3778)+6*s(3779)+12*s(3780)+12*s(3781)+48*s(3782)+42*s(3783)+6*s(3784)+10*s(3796)+50*s(3797)+80*s(3798)+60*s(3799)+10*s(3800)+30*s(3801)+30*s(3802)+40*s(3803)+40*s(3804)+40*s(3805)+10*s(3812)+10*s(3818)+20*s(3826)+20*s(3827)+80*s(3828)+30*s(3829)+20*s(3830)+230*s(3831)+40*s(3832)+10*s(3833)+60*s(3834)+60*s(3836)+20*s(3837)+60*s(3839)+120*s(3840)+30*s(3841)+10*s(3842)+20*s(3843)+20*s(3844)+80*s(3845)+70*s(3846)+10*s(3847)+10*s(3859)+50*s(3860)+80*s(3861)+60*s(3862)+10*s(3863)+30*s(3864)+30*s(3865)+40*s(3866)+40*s(3867)+40*s(3868)+10*s(3875)+10*s(3881)+20*s(3889)+20*s(3890)+80*s(3891)+30*s(3892)+20*s(3893)+230*s(3894)+40*s(3895)+10*s(3896)+60*s(3897)+60*s(3899)+20*s(3900)+60*s(3902)+120*s(3903)+30*s(3904)+10*s(3905)+20*s(3906)+20*s(3907)+80*s(3908)+70*s(3909)+10*s(3910)+1 Such that:aux(262) =< V1 aux(263) =< 2*V1 aux(264) =< 2*V1+1 aux(265) =< V1/2 aux(266) =< 2/3*V1 aux(267) =< 2/3*V1+1/3 aux(268) =< 3/5*V1 aux(269) =< 3/8*V1 aux(270) =< 4/5*V1 aux(271) =< 4/7*V1 aux(272) =< 4/9*V1 aux(273) =< V aux(274) =< 2*V aux(275) =< 2*V+1 aux(276) =< V/2 aux(277) =< 2/3*V aux(278) =< 2/3*V+1/3 aux(279) =< 3/5*V aux(280) =< 3/8*V aux(281) =< 4/5*V aux(282) =< 4/7*V aux(283) =< 4/9*V aux(284) =< V2 aux(285) =< 2*V2 aux(286) =< 2*V2+1 aux(287) =< V2/2 aux(288) =< 2/3*V2 aux(289) =< 2/3*V2+1/3 aux(290) =< 3/5*V2 aux(291) =< 3/8*V2 aux(292) =< 4/5*V2 aux(293) =< 4/7*V2 aux(294) =< 4/9*V2 s(3727) =< aux(267) s(3790) =< aux(278) s(3853) =< aux(289) s(3859) =< aux(284) s(3860) =< aux(284) s(3861) =< aux(284) s(3862) =< aux(284) s(3863) =< aux(284) s(3864) =< aux(284) s(3865) =< aux(284) s(3853) =< aux(284) s(3853) =< aux(286) s(3866) =< aux(287) s(3862) =< aux(288) s(3867) =< aux(290) s(3868) =< aux(291) s(3864) =< aux(292) s(3869) =< aux(293) s(3861) =< aux(293) s(3860) =< aux(294) s(3870) =< aux(285)+1 s(3871) =< aux(285)+3 s(3872) =< aux(285) s(3873) =< aux(285)+2 s(3874) =< aux(285)-1 s(3864) =< aux(286)*(1/5)+aux(292) s(3865) =< aux(286)*(1/5)+aux(292) s(3862) =< aux(286)*(1/3)+aux(288) s(3863) =< aux(286)*(1/3)+aux(288) s(3864) =< aux(286)*(1/3)+aux(288) s(3865) =< aux(286)*(1/3)+aux(288) s(3861) =< aux(286)*(3/7)+aux(293) s(3862) =< aux(286)*(3/7)+aux(293) s(3863) =< aux(286)*(3/7)+aux(293) s(3864) =< aux(286)*(3/7)+aux(293) s(3865) =< aux(286)*(3/7)+aux(293) s(3869) =< aux(286)*(3/7)+aux(293) s(3860) =< aux(286)*(5/9)+s(3853)*(1/9)+aux(294) s(3861) =< aux(286)*(5/9)+s(3853)*(1/9)+aux(294) s(3862) =< aux(286)*(5/9)+s(3853)*(1/9)+aux(294) s(3863) =< aux(286)*(5/9)+s(3853)*(1/9)+aux(294) s(3864) =< aux(286)*(5/9)+s(3853)*(1/9)+aux(294) s(3865) =< aux(286)*(5/9)+s(3853)*(1/9)+aux(294) s(3867) =< aux(286)*(1/5)+aux(290) s(3859) =< aux(286)*(1/5)+aux(290) s(3866) =< aux(286)*(1/4)+aux(287) s(3867) =< aux(286)*(1/4)+aux(287) s(3859) =< aux(286)*(1/4)+aux(287) s(3868) =< aux(286)*(5/16)+aux(291) s(3866) =< aux(286)*(5/16)+aux(291) s(3867) =< aux(286)*(5/16)+aux(291) s(3859) =< aux(286)*(5/16)+aux(291) s(3875) =< s(3865)*s(3870) s(3876) =< s(3865)*s(3870) s(3877) =< s(3865)*s(3871) s(3878) =< s(3864)*s(3871) s(3879) =< s(3862)*s(3872) s(3880) =< s(3862)*s(3873) s(3881) =< s(3862)*s(3872) s(3882) =< s(3861)*s(3872) s(3883) =< s(3861)*s(3873) s(3884) =< s(3860)*s(3870) s(3885) =< s(3867)*s(3874) s(3886) =< s(3867)*s(3872) s(3887) =< s(3866)*s(3872) s(3888) =< s(3868)*s(3870) s(3889) =< s(3876) s(3890) =< s(3877) s(3891) =< s(3878) s(3892) =< s(3879) s(3893) =< s(3880) s(3894) =< s(3883) s(3895) =< s(3894)*s(3873) s(3896) =< s(3895)*s(3873) s(3897) =< s(3882) s(3898) =< s(3897)*aux(285) s(3899) =< s(3898) s(3900) =< s(3869) s(3901) =< s(3894)*s(3873) s(3902) =< s(3901) s(3903) =< s(3884) s(3904) =< s(3903)*s(3870) s(3905) =< s(3904)*s(3870) s(3906) =< s(3886) s(3907) =< s(3885) s(3908) =< s(3887) s(3909) =< s(3888) s(3910) =< s(3909)*s(3870) s(3796) =< aux(273) s(3797) =< aux(273) s(3798) =< aux(273) s(3799) =< aux(273) s(3800) =< aux(273) s(3801) =< aux(273) s(3802) =< aux(273) s(3790) =< aux(273) s(3790) =< aux(275) s(3803) =< aux(276) s(3799) =< aux(277) s(3804) =< aux(279) s(3805) =< aux(280) s(3801) =< aux(281) s(3806) =< aux(282) s(3798) =< aux(282) s(3797) =< aux(283) s(3807) =< aux(274)+1 s(3808) =< aux(274)+3 s(3809) =< aux(274) s(3810) =< aux(274)+2 s(3811) =< aux(274)-1 s(3801) =< aux(275)*(1/5)+aux(281) s(3802) =< aux(275)*(1/5)+aux(281) s(3799) =< aux(275)*(1/3)+aux(277) s(3800) =< aux(275)*(1/3)+aux(277) s(3801) =< aux(275)*(1/3)+aux(277) s(3802) =< aux(275)*(1/3)+aux(277) s(3798) =< aux(275)*(3/7)+aux(282) s(3799) =< aux(275)*(3/7)+aux(282) s(3800) =< aux(275)*(3/7)+aux(282) s(3801) =< aux(275)*(3/7)+aux(282) s(3802) =< aux(275)*(3/7)+aux(282) s(3806) =< aux(275)*(3/7)+aux(282) s(3797) =< aux(275)*(5/9)+s(3790)*(1/9)+aux(283) s(3798) =< aux(275)*(5/9)+s(3790)*(1/9)+aux(283) s(3799) =< aux(275)*(5/9)+s(3790)*(1/9)+aux(283) s(3800) =< aux(275)*(5/9)+s(3790)*(1/9)+aux(283) s(3801) =< aux(275)*(5/9)+s(3790)*(1/9)+aux(283) s(3802) =< aux(275)*(5/9)+s(3790)*(1/9)+aux(283) s(3804) =< aux(275)*(1/5)+aux(279) s(3796) =< aux(275)*(1/5)+aux(279) s(3803) =< aux(275)*(1/4)+aux(276) s(3804) =< aux(275)*(1/4)+aux(276) s(3796) =< aux(275)*(1/4)+aux(276) s(3805) =< aux(275)*(5/16)+aux(280) s(3803) =< aux(275)*(5/16)+aux(280) s(3804) =< aux(275)*(5/16)+aux(280) s(3796) =< aux(275)*(5/16)+aux(280) s(3812) =< s(3802)*s(3807) s(3813) =< s(3802)*s(3807) s(3814) =< s(3802)*s(3808) s(3815) =< s(3801)*s(3808) s(3816) =< s(3799)*s(3809) s(3817) =< s(3799)*s(3810) s(3818) =< s(3799)*s(3809) s(3819) =< s(3798)*s(3809) s(3820) =< s(3798)*s(3810) s(3821) =< s(3797)*s(3807) s(3822) =< s(3804)*s(3811) s(3823) =< s(3804)*s(3809) s(3824) =< s(3803)*s(3809) s(3825) =< s(3805)*s(3807) s(3826) =< s(3813) s(3827) =< s(3814) s(3828) =< s(3815) s(3829) =< s(3816) s(3830) =< s(3817) s(3831) =< s(3820) s(3832) =< s(3831)*s(3810) s(3833) =< s(3832)*s(3810) s(3834) =< s(3819) s(3835) =< s(3834)*aux(274) s(3836) =< s(3835) s(3837) =< s(3806) s(3838) =< s(3831)*s(3810) s(3839) =< s(3838) s(3840) =< s(3821) s(3841) =< s(3840)*s(3807) s(3842) =< s(3841)*s(3807) s(3843) =< s(3823) s(3844) =< s(3822) s(3845) =< s(3824) s(3846) =< s(3825) s(3847) =< s(3846)*s(3807) s(3733) =< aux(262) s(3734) =< aux(262) s(3735) =< aux(262) s(3736) =< aux(262) s(3737) =< aux(262) s(3738) =< aux(262) s(3739) =< aux(262) s(3727) =< aux(262) s(3727) =< aux(264) s(3740) =< aux(265) s(3736) =< aux(266) s(3741) =< aux(268) s(3742) =< aux(269) s(3738) =< aux(270) s(3743) =< aux(271) s(3735) =< aux(271) s(3734) =< aux(272) s(3744) =< aux(263)+1 s(3745) =< aux(263)+3 s(3746) =< aux(263) s(3747) =< aux(263)+2 s(3748) =< aux(263)-1 s(3738) =< aux(264)*(1/5)+aux(270) s(3739) =< aux(264)*(1/5)+aux(270) s(3736) =< aux(264)*(1/3)+aux(266) s(3737) =< aux(264)*(1/3)+aux(266) s(3738) =< aux(264)*(1/3)+aux(266) s(3739) =< aux(264)*(1/3)+aux(266) s(3735) =< aux(264)*(3/7)+aux(271) s(3736) =< aux(264)*(3/7)+aux(271) s(3737) =< aux(264)*(3/7)+aux(271) s(3738) =< aux(264)*(3/7)+aux(271) s(3739) =< aux(264)*(3/7)+aux(271) s(3743) =< aux(264)*(3/7)+aux(271) s(3734) =< aux(264)*(5/9)+s(3727)*(1/9)+aux(272) s(3735) =< aux(264)*(5/9)+s(3727)*(1/9)+aux(272) s(3736) =< aux(264)*(5/9)+s(3727)*(1/9)+aux(272) s(3737) =< aux(264)*(5/9)+s(3727)*(1/9)+aux(272) s(3738) =< aux(264)*(5/9)+s(3727)*(1/9)+aux(272) s(3739) =< aux(264)*(5/9)+s(3727)*(1/9)+aux(272) s(3741) =< aux(264)*(1/5)+aux(268) s(3733) =< aux(264)*(1/5)+aux(268) s(3740) =< aux(264)*(1/4)+aux(265) s(3741) =< aux(264)*(1/4)+aux(265) s(3733) =< aux(264)*(1/4)+aux(265) s(3742) =< aux(264)*(5/16)+aux(269) s(3740) =< aux(264)*(5/16)+aux(269) s(3741) =< aux(264)*(5/16)+aux(269) s(3733) =< aux(264)*(5/16)+aux(269) s(3749) =< s(3739)*s(3744) s(3750) =< s(3739)*s(3744) s(3751) =< s(3739)*s(3745) s(3752) =< s(3738)*s(3745) s(3753) =< s(3736)*s(3746) s(3754) =< s(3736)*s(3747) s(3755) =< s(3736)*s(3746) s(3756) =< s(3735)*s(3746) s(3757) =< s(3735)*s(3747) s(3758) =< s(3734)*s(3744) s(3759) =< s(3741)*s(3748) s(3760) =< s(3741)*s(3746) s(3761) =< s(3740)*s(3746) s(3762) =< s(3742)*s(3744) s(3763) =< s(3750) s(3764) =< s(3751) s(3765) =< s(3752) s(3766) =< s(3753) s(3767) =< s(3754) s(3768) =< s(3757) s(3769) =< s(3768)*s(3747) s(3770) =< s(3769)*s(3747) s(3771) =< s(3756) s(3772) =< s(3771)*aux(263) s(3773) =< s(3772) s(3774) =< s(3743) s(3775) =< s(3768)*s(3747) s(3776) =< s(3775) s(3777) =< s(3758) s(3778) =< s(3777)*s(3744) s(3779) =< s(3778)*s(3744) s(3780) =< s(3760) s(3781) =< s(3759) s(3782) =< s(3761) s(3783) =< s(3762) s(3784) =< s(3783)*s(3744) with precondition: [Out=0,V1>=0,V>=0,V2>=0] * Chain [76]: 3*s(5371)+15*s(5372)+24*s(5373)+18*s(5374)+3*s(5375)+9*s(5376)+9*s(5377)+12*s(5378)+12*s(5379)+12*s(5380)+3*s(5387)+3*s(5393)+6*s(5401)+6*s(5402)+24*s(5403)+9*s(5404)+6*s(5405)+69*s(5406)+12*s(5407)+3*s(5408)+18*s(5409)+18*s(5411)+6*s(5412)+18*s(5414)+36*s(5415)+9*s(5416)+3*s(5417)+6*s(5418)+6*s(5419)+24*s(5420)+21*s(5421)+3*s(5422)+5*s(5434)+25*s(5435)+40*s(5436)+30*s(5437)+5*s(5438)+15*s(5439)+15*s(5440)+20*s(5441)+20*s(5442)+20*s(5443)+5*s(5450)+5*s(5456)+10*s(5464)+10*s(5465)+40*s(5466)+15*s(5467)+10*s(5468)+115*s(5469)+20*s(5470)+5*s(5471)+30*s(5472)+30*s(5474)+10*s(5475)+30*s(5477)+60*s(5478)+15*s(5479)+5*s(5480)+10*s(5481)+10*s(5482)+40*s(5483)+35*s(5484)+5*s(5485)+1 Such that:aux(295) =< V1 aux(296) =< 2*V1 aux(297) =< 2*V1+1 aux(298) =< V1/2 aux(299) =< 2/3*V1 aux(300) =< 2/3*V1+1/3 aux(301) =< 3/5*V1 aux(302) =< 3/8*V1 aux(303) =< 4/5*V1 aux(304) =< 4/7*V1 aux(305) =< 4/9*V1 aux(306) =< V aux(307) =< 2*V aux(308) =< 2*V+1 aux(309) =< V/2 aux(310) =< 2/3*V aux(311) =< 2/3*V+1/3 aux(312) =< 3/5*V aux(313) =< 3/8*V aux(314) =< 4/5*V aux(315) =< 4/7*V aux(316) =< 4/9*V s(5365) =< aux(300) s(5428) =< aux(311) s(5434) =< aux(306) s(5435) =< aux(306) s(5436) =< aux(306) s(5437) =< aux(306) s(5438) =< aux(306) s(5439) =< aux(306) s(5440) =< aux(306) s(5428) =< aux(306) s(5428) =< aux(308) s(5441) =< aux(309) s(5437) =< aux(310) s(5442) =< aux(312) s(5443) =< aux(313) s(5439) =< aux(314) s(5444) =< aux(315) s(5436) =< aux(315) s(5435) =< aux(316) s(5445) =< aux(307)+1 s(5446) =< aux(307)+3 s(5447) =< aux(307) s(5448) =< aux(307)+2 s(5449) =< aux(307)-1 s(5439) =< aux(308)*(1/5)+aux(314) s(5440) =< aux(308)*(1/5)+aux(314) s(5437) =< aux(308)*(1/3)+aux(310) s(5438) =< aux(308)*(1/3)+aux(310) s(5439) =< aux(308)*(1/3)+aux(310) s(5440) =< aux(308)*(1/3)+aux(310) s(5436) =< aux(308)*(3/7)+aux(315) s(5437) =< aux(308)*(3/7)+aux(315) s(5438) =< aux(308)*(3/7)+aux(315) s(5439) =< aux(308)*(3/7)+aux(315) s(5440) =< aux(308)*(3/7)+aux(315) s(5444) =< aux(308)*(3/7)+aux(315) s(5435) =< aux(308)*(5/9)+s(5428)*(1/9)+aux(316) s(5436) =< aux(308)*(5/9)+s(5428)*(1/9)+aux(316) s(5437) =< aux(308)*(5/9)+s(5428)*(1/9)+aux(316) s(5438) =< aux(308)*(5/9)+s(5428)*(1/9)+aux(316) s(5439) =< aux(308)*(5/9)+s(5428)*(1/9)+aux(316) s(5440) =< aux(308)*(5/9)+s(5428)*(1/9)+aux(316) s(5442) =< aux(308)*(1/5)+aux(312) s(5434) =< aux(308)*(1/5)+aux(312) s(5441) =< aux(308)*(1/4)+aux(309) s(5442) =< aux(308)*(1/4)+aux(309) s(5434) =< aux(308)*(1/4)+aux(309) s(5443) =< aux(308)*(5/16)+aux(313) s(5441) =< aux(308)*(5/16)+aux(313) s(5442) =< aux(308)*(5/16)+aux(313) s(5434) =< aux(308)*(5/16)+aux(313) s(5450) =< s(5440)*s(5445) s(5451) =< s(5440)*s(5445) s(5452) =< s(5440)*s(5446) s(5453) =< s(5439)*s(5446) s(5454) =< s(5437)*s(5447) s(5455) =< s(5437)*s(5448) s(5456) =< s(5437)*s(5447) s(5457) =< s(5436)*s(5447) s(5458) =< s(5436)*s(5448) s(5459) =< s(5435)*s(5445) s(5460) =< s(5442)*s(5449) s(5461) =< s(5442)*s(5447) s(5462) =< s(5441)*s(5447) s(5463) =< s(5443)*s(5445) s(5464) =< s(5451) s(5465) =< s(5452) s(5466) =< s(5453) s(5467) =< s(5454) s(5468) =< s(5455) s(5469) =< s(5458) s(5470) =< s(5469)*s(5448) s(5471) =< s(5470)*s(5448) s(5472) =< s(5457) s(5473) =< s(5472)*aux(307) s(5474) =< s(5473) s(5475) =< s(5444) s(5476) =< s(5469)*s(5448) s(5477) =< s(5476) s(5478) =< s(5459) s(5479) =< s(5478)*s(5445) s(5480) =< s(5479)*s(5445) s(5481) =< s(5461) s(5482) =< s(5460) s(5483) =< s(5462) s(5484) =< s(5463) s(5485) =< s(5484)*s(5445) s(5371) =< aux(295) s(5372) =< aux(295) s(5373) =< aux(295) s(5374) =< aux(295) s(5375) =< aux(295) s(5376) =< aux(295) s(5377) =< aux(295) s(5365) =< aux(295) s(5365) =< aux(297) s(5378) =< aux(298) s(5374) =< aux(299) s(5379) =< aux(301) s(5380) =< aux(302) s(5376) =< aux(303) s(5381) =< aux(304) s(5373) =< aux(304) s(5372) =< aux(305) s(5382) =< aux(296)+1 s(5383) =< aux(296)+3 s(5384) =< aux(296) s(5385) =< aux(296)+2 s(5386) =< aux(296)-1 s(5376) =< aux(297)*(1/5)+aux(303) s(5377) =< aux(297)*(1/5)+aux(303) s(5374) =< aux(297)*(1/3)+aux(299) s(5375) =< aux(297)*(1/3)+aux(299) s(5376) =< aux(297)*(1/3)+aux(299) s(5377) =< aux(297)*(1/3)+aux(299) s(5373) =< aux(297)*(3/7)+aux(304) s(5374) =< aux(297)*(3/7)+aux(304) s(5375) =< aux(297)*(3/7)+aux(304) s(5376) =< aux(297)*(3/7)+aux(304) s(5377) =< aux(297)*(3/7)+aux(304) s(5381) =< aux(297)*(3/7)+aux(304) s(5372) =< aux(297)*(5/9)+s(5365)*(1/9)+aux(305) s(5373) =< aux(297)*(5/9)+s(5365)*(1/9)+aux(305) s(5374) =< aux(297)*(5/9)+s(5365)*(1/9)+aux(305) s(5375) =< aux(297)*(5/9)+s(5365)*(1/9)+aux(305) s(5376) =< aux(297)*(5/9)+s(5365)*(1/9)+aux(305) s(5377) =< aux(297)*(5/9)+s(5365)*(1/9)+aux(305) s(5379) =< aux(297)*(1/5)+aux(301) s(5371) =< aux(297)*(1/5)+aux(301) s(5378) =< aux(297)*(1/4)+aux(298) s(5379) =< aux(297)*(1/4)+aux(298) s(5371) =< aux(297)*(1/4)+aux(298) s(5380) =< aux(297)*(5/16)+aux(302) s(5378) =< aux(297)*(5/16)+aux(302) s(5379) =< aux(297)*(5/16)+aux(302) s(5371) =< aux(297)*(5/16)+aux(302) s(5387) =< s(5377)*s(5382) s(5388) =< s(5377)*s(5382) s(5389) =< s(5377)*s(5383) s(5390) =< s(5376)*s(5383) s(5391) =< s(5374)*s(5384) s(5392) =< s(5374)*s(5385) s(5393) =< s(5374)*s(5384) s(5394) =< s(5373)*s(5384) s(5395) =< s(5373)*s(5385) s(5396) =< s(5372)*s(5382) s(5397) =< s(5379)*s(5386) s(5398) =< s(5379)*s(5384) s(5399) =< s(5378)*s(5384) s(5400) =< s(5380)*s(5382) s(5401) =< s(5388) s(5402) =< s(5389) s(5403) =< s(5390) s(5404) =< s(5391) s(5405) =< s(5392) s(5406) =< s(5395) s(5407) =< s(5406)*s(5385) s(5408) =< s(5407)*s(5385) s(5409) =< s(5394) s(5410) =< s(5409)*aux(296) s(5411) =< s(5410) s(5412) =< s(5381) s(5413) =< s(5406)*s(5385) s(5414) =< s(5413) s(5415) =< s(5396) s(5416) =< s(5415)*s(5382) s(5417) =< s(5416)*s(5382) s(5418) =< s(5398) s(5419) =< s(5397) s(5420) =< s(5399) s(5421) =< s(5400) s(5422) =< s(5421)*s(5382) with precondition: [V2=2,Out=0,V1>=0,V>=0] * Chain [75]: 6*s(5875)+30*s(5876)+48*s(5877)+36*s(5878)+6*s(5879)+18*s(5880)+18*s(5881)+24*s(5882)+24*s(5883)+24*s(5884)+6*s(5891)+6*s(5897)+12*s(5905)+12*s(5906)+48*s(5907)+18*s(5908)+12*s(5909)+138*s(5910)+24*s(5911)+6*s(5912)+36*s(5913)+36*s(5915)+12*s(5916)+36*s(5918)+72*s(5919)+18*s(5920)+6*s(5921)+12*s(5922)+12*s(5923)+48*s(5924)+42*s(5925)+6*s(5926)+3*s(5938)+15*s(5939)+24*s(5940)+18*s(5941)+3*s(5942)+9*s(5943)+9*s(5944)+12*s(5945)+12*s(5946)+12*s(5947)+3*s(5954)+3*s(5960)+6*s(5968)+6*s(5969)+24*s(5970)+9*s(5971)+6*s(5972)+69*s(5973)+12*s(5974)+3*s(5975)+18*s(5976)+18*s(5978)+6*s(5979)+18*s(5981)+36*s(5982)+9*s(5983)+3*s(5984)+6*s(5985)+6*s(5986)+24*s(5987)+21*s(5988)+3*s(5989)+1 Such that:aux(317) =< V1 aux(318) =< 2*V1 aux(319) =< 2*V1+1 aux(320) =< V1/2 aux(321) =< 2/3*V1 aux(322) =< 2/3*V1+1/3 aux(323) =< 3/5*V1 aux(324) =< 3/8*V1 aux(325) =< 4/5*V1 aux(326) =< 4/7*V1 aux(327) =< 4/9*V1 aux(328) =< V2 aux(329) =< 2*V2 aux(330) =< 2*V2+1 aux(331) =< V2/2 aux(332) =< 2/3*V2 aux(333) =< 2/3*V2+1/3 aux(334) =< 3/5*V2 aux(335) =< 3/8*V2 aux(336) =< 4/5*V2 aux(337) =< 4/7*V2 aux(338) =< 4/9*V2 s(5869) =< aux(322) s(5932) =< aux(333) s(5938) =< aux(328) s(5939) =< aux(328) s(5940) =< aux(328) s(5941) =< aux(328) s(5942) =< aux(328) s(5943) =< aux(328) s(5944) =< aux(328) s(5932) =< aux(328) s(5932) =< aux(330) s(5945) =< aux(331) s(5941) =< aux(332) s(5946) =< aux(334) s(5947) =< aux(335) s(5943) =< aux(336) s(5948) =< aux(337) s(5940) =< aux(337) s(5939) =< aux(338) s(5949) =< aux(329)+1 s(5950) =< aux(329)+3 s(5951) =< aux(329) s(5952) =< aux(329)+2 s(5953) =< aux(329)-1 s(5943) =< aux(330)*(1/5)+aux(336) s(5944) =< aux(330)*(1/5)+aux(336) s(5941) =< aux(330)*(1/3)+aux(332) s(5942) =< aux(330)*(1/3)+aux(332) s(5943) =< aux(330)*(1/3)+aux(332) s(5944) =< aux(330)*(1/3)+aux(332) s(5940) =< aux(330)*(3/7)+aux(337) s(5941) =< aux(330)*(3/7)+aux(337) s(5942) =< aux(330)*(3/7)+aux(337) s(5943) =< aux(330)*(3/7)+aux(337) s(5944) =< aux(330)*(3/7)+aux(337) s(5948) =< aux(330)*(3/7)+aux(337) s(5939) =< aux(330)*(5/9)+s(5932)*(1/9)+aux(338) s(5940) =< aux(330)*(5/9)+s(5932)*(1/9)+aux(338) s(5941) =< aux(330)*(5/9)+s(5932)*(1/9)+aux(338) s(5942) =< aux(330)*(5/9)+s(5932)*(1/9)+aux(338) s(5943) =< aux(330)*(5/9)+s(5932)*(1/9)+aux(338) s(5944) =< aux(330)*(5/9)+s(5932)*(1/9)+aux(338) s(5946) =< aux(330)*(1/5)+aux(334) s(5938) =< aux(330)*(1/5)+aux(334) s(5945) =< aux(330)*(1/4)+aux(331) s(5946) =< aux(330)*(1/4)+aux(331) s(5938) =< aux(330)*(1/4)+aux(331) s(5947) =< aux(330)*(5/16)+aux(335) s(5945) =< aux(330)*(5/16)+aux(335) s(5946) =< aux(330)*(5/16)+aux(335) s(5938) =< aux(330)*(5/16)+aux(335) s(5954) =< s(5944)*s(5949) s(5955) =< s(5944)*s(5949) s(5956) =< s(5944)*s(5950) s(5957) =< s(5943)*s(5950) s(5958) =< s(5941)*s(5951) s(5959) =< s(5941)*s(5952) s(5960) =< s(5941)*s(5951) s(5961) =< s(5940)*s(5951) s(5962) =< s(5940)*s(5952) s(5963) =< s(5939)*s(5949) s(5964) =< s(5946)*s(5953) s(5965) =< s(5946)*s(5951) s(5966) =< s(5945)*s(5951) s(5967) =< s(5947)*s(5949) s(5968) =< s(5955) s(5969) =< s(5956) s(5970) =< s(5957) s(5971) =< s(5958) s(5972) =< s(5959) s(5973) =< s(5962) s(5974) =< s(5973)*s(5952) s(5975) =< s(5974)*s(5952) s(5976) =< s(5961) s(5977) =< s(5976)*aux(329) s(5978) =< s(5977) s(5979) =< s(5948) s(5980) =< s(5973)*s(5952) s(5981) =< s(5980) s(5982) =< s(5963) s(5983) =< s(5982)*s(5949) s(5984) =< s(5983)*s(5949) s(5985) =< s(5965) s(5986) =< s(5964) s(5987) =< s(5966) s(5988) =< s(5967) s(5989) =< s(5988)*s(5949) s(5875) =< aux(317) s(5876) =< aux(317) s(5877) =< aux(317) s(5878) =< aux(317) s(5879) =< aux(317) s(5880) =< aux(317) s(5881) =< aux(317) s(5869) =< aux(317) s(5869) =< aux(319) s(5882) =< aux(320) s(5878) =< aux(321) s(5883) =< aux(323) s(5884) =< aux(324) s(5880) =< aux(325) s(5885) =< aux(326) s(5877) =< aux(326) s(5876) =< aux(327) s(5886) =< aux(318)+1 s(5887) =< aux(318)+3 s(5888) =< aux(318) s(5889) =< aux(318)+2 s(5890) =< aux(318)-1 s(5880) =< aux(319)*(1/5)+aux(325) s(5881) =< aux(319)*(1/5)+aux(325) s(5878) =< aux(319)*(1/3)+aux(321) s(5879) =< aux(319)*(1/3)+aux(321) s(5880) =< aux(319)*(1/3)+aux(321) s(5881) =< aux(319)*(1/3)+aux(321) s(5877) =< aux(319)*(3/7)+aux(326) s(5878) =< aux(319)*(3/7)+aux(326) s(5879) =< aux(319)*(3/7)+aux(326) s(5880) =< aux(319)*(3/7)+aux(326) s(5881) =< aux(319)*(3/7)+aux(326) s(5885) =< aux(319)*(3/7)+aux(326) s(5876) =< aux(319)*(5/9)+s(5869)*(1/9)+aux(327) s(5877) =< aux(319)*(5/9)+s(5869)*(1/9)+aux(327) s(5878) =< aux(319)*(5/9)+s(5869)*(1/9)+aux(327) s(5879) =< aux(319)*(5/9)+s(5869)*(1/9)+aux(327) s(5880) =< aux(319)*(5/9)+s(5869)*(1/9)+aux(327) s(5881) =< aux(319)*(5/9)+s(5869)*(1/9)+aux(327) s(5883) =< aux(319)*(1/5)+aux(323) s(5875) =< aux(319)*(1/5)+aux(323) s(5882) =< aux(319)*(1/4)+aux(320) s(5883) =< aux(319)*(1/4)+aux(320) s(5875) =< aux(319)*(1/4)+aux(320) s(5884) =< aux(319)*(5/16)+aux(324) s(5882) =< aux(319)*(5/16)+aux(324) s(5883) =< aux(319)*(5/16)+aux(324) s(5875) =< aux(319)*(5/16)+aux(324) s(5891) =< s(5881)*s(5886) s(5892) =< s(5881)*s(5886) s(5893) =< s(5881)*s(5887) s(5894) =< s(5880)*s(5887) s(5895) =< s(5878)*s(5888) s(5896) =< s(5878)*s(5889) s(5897) =< s(5878)*s(5888) s(5898) =< s(5877)*s(5888) s(5899) =< s(5877)*s(5889) s(5900) =< s(5876)*s(5886) s(5901) =< s(5883)*s(5890) s(5902) =< s(5883)*s(5888) s(5903) =< s(5882)*s(5888) s(5904) =< s(5884)*s(5886) s(5905) =< s(5892) s(5906) =< s(5893) s(5907) =< s(5894) s(5908) =< s(5895) s(5909) =< s(5896) s(5910) =< s(5899) s(5911) =< s(5910)*s(5889) s(5912) =< s(5911)*s(5889) s(5913) =< s(5898) s(5914) =< s(5913)*aux(318) s(5915) =< s(5914) s(5916) =< s(5885) s(5917) =< s(5910)*s(5889) s(5918) =< s(5917) s(5919) =< s(5900) s(5920) =< s(5919)*s(5886) s(5921) =< s(5920)*s(5886) s(5922) =< s(5902) s(5923) =< s(5901) s(5924) =< s(5903) s(5925) =< s(5904) s(5926) =< s(5925)*s(5886) with precondition: [V=2,Out=0,V1>=0,V2>=0] * Chain [74]: 5*s(6442)+25*s(6443)+40*s(6444)+30*s(6445)+5*s(6446)+15*s(6447)+15*s(6448)+20*s(6449)+20*s(6450)+20*s(6451)+5*s(6458)+5*s(6464)+10*s(6472)+10*s(6473)+40*s(6474)+15*s(6475)+10*s(6476)+115*s(6477)+20*s(6478)+5*s(6479)+30*s(6480)+30*s(6482)+10*s(6483)+30*s(6485)+60*s(6486)+15*s(6487)+5*s(6488)+10*s(6489)+10*s(6490)+40*s(6491)+35*s(6492)+5*s(6493)+2*s(6505)+10*s(6506)+16*s(6507)+12*s(6508)+2*s(6509)+6*s(6510)+6*s(6511)+8*s(6512)+8*s(6513)+8*s(6514)+2*s(6521)+2*s(6527)+4*s(6535)+4*s(6536)+16*s(6537)+6*s(6538)+4*s(6539)+46*s(6540)+8*s(6541)+2*s(6542)+12*s(6543)+12*s(6545)+4*s(6546)+12*s(6548)+24*s(6549)+6*s(6550)+2*s(6551)+4*s(6552)+4*s(6553)+16*s(6554)+14*s(6555)+2*s(6556)+2*s(6568)+10*s(6569)+16*s(6570)+12*s(6571)+2*s(6572)+6*s(6573)+6*s(6574)+8*s(6575)+8*s(6576)+8*s(6577)+2*s(6584)+2*s(6590)+4*s(6598)+4*s(6599)+16*s(6600)+6*s(6601)+4*s(6602)+46*s(6603)+8*s(6604)+2*s(6605)+12*s(6606)+12*s(6608)+4*s(6609)+12*s(6611)+24*s(6612)+6*s(6613)+2*s(6614)+4*s(6615)+4*s(6616)+16*s(6617)+14*s(6618)+2*s(6619)+4*s(6622)+4*s(6623)+6*s(6882)+2*s(6950)+4 Such that:s(6948) =< 2 aux(343) =< 1 aux(344) =< V1 aux(345) =< 2*V1 aux(346) =< 2*V1+1 aux(347) =< V1/2 aux(348) =< 2/3*V1 aux(349) =< 2/3*V1+1/3 aux(350) =< 3/5*V1 aux(351) =< 3/8*V1 aux(352) =< 4/5*V1 aux(353) =< 4/7*V1 aux(354) =< 4/9*V1 aux(355) =< V aux(356) =< 2*V aux(357) =< 2*V+1 aux(358) =< V/2 aux(359) =< 2/3*V aux(360) =< 2/3*V+1/3 aux(361) =< 3/5*V aux(362) =< 3/8*V aux(363) =< 4/5*V aux(364) =< 4/7*V aux(365) =< 4/9*V aux(366) =< V2 aux(367) =< 2*V2 aux(368) =< 2*V2+1 aux(369) =< V2/2 aux(370) =< 2/3*V2 aux(371) =< 2/3*V2+1/3 aux(372) =< 3/5*V2 aux(373) =< 3/8*V2 aux(374) =< 4/5*V2 aux(375) =< 4/7*V2 aux(376) =< 4/9*V2 s(6436) =< aux(349) s(6499) =< aux(360) s(6562) =< aux(371) s(6882) =< aux(343) s(6623) =< aux(367) s(6568) =< aux(366) s(6569) =< aux(366) s(6570) =< aux(366) s(6571) =< aux(366) s(6572) =< aux(366) s(6573) =< aux(366) s(6574) =< aux(366) s(6562) =< aux(366) s(6562) =< aux(368) s(6575) =< aux(369) s(6571) =< aux(370) s(6576) =< aux(372) s(6577) =< aux(373) s(6573) =< aux(374) s(6578) =< aux(375) s(6570) =< aux(375) s(6569) =< aux(376) s(6579) =< aux(367)+1 s(6580) =< aux(367)+3 s(6581) =< aux(367) s(6582) =< aux(367)+2 s(6583) =< aux(367)-1 s(6573) =< aux(368)*(1/5)+aux(374) s(6574) =< aux(368)*(1/5)+aux(374) s(6571) =< aux(368)*(1/3)+aux(370) s(6572) =< aux(368)*(1/3)+aux(370) s(6573) =< aux(368)*(1/3)+aux(370) s(6574) =< aux(368)*(1/3)+aux(370) s(6570) =< aux(368)*(3/7)+aux(375) s(6571) =< aux(368)*(3/7)+aux(375) s(6572) =< aux(368)*(3/7)+aux(375) s(6573) =< aux(368)*(3/7)+aux(375) s(6574) =< aux(368)*(3/7)+aux(375) s(6578) =< aux(368)*(3/7)+aux(375) s(6569) =< aux(368)*(5/9)+s(6562)*(1/9)+aux(376) s(6570) =< aux(368)*(5/9)+s(6562)*(1/9)+aux(376) s(6571) =< aux(368)*(5/9)+s(6562)*(1/9)+aux(376) s(6572) =< aux(368)*(5/9)+s(6562)*(1/9)+aux(376) s(6573) =< aux(368)*(5/9)+s(6562)*(1/9)+aux(376) s(6574) =< aux(368)*(5/9)+s(6562)*(1/9)+aux(376) s(6576) =< aux(368)*(1/5)+aux(372) s(6568) =< aux(368)*(1/5)+aux(372) s(6575) =< aux(368)*(1/4)+aux(369) s(6576) =< aux(368)*(1/4)+aux(369) s(6568) =< aux(368)*(1/4)+aux(369) s(6577) =< aux(368)*(5/16)+aux(373) s(6575) =< aux(368)*(5/16)+aux(373) s(6576) =< aux(368)*(5/16)+aux(373) s(6568) =< aux(368)*(5/16)+aux(373) s(6584) =< s(6574)*s(6579) s(6585) =< s(6574)*s(6579) s(6586) =< s(6574)*s(6580) s(6587) =< s(6573)*s(6580) s(6588) =< s(6571)*s(6581) s(6589) =< s(6571)*s(6582) s(6590) =< s(6571)*s(6581) s(6591) =< s(6570)*s(6581) s(6592) =< s(6570)*s(6582) s(6593) =< s(6569)*s(6579) s(6594) =< s(6576)*s(6583) s(6595) =< s(6576)*s(6581) s(6596) =< s(6575)*s(6581) s(6597) =< s(6577)*s(6579) s(6598) =< s(6585) s(6599) =< s(6586) s(6600) =< s(6587) s(6601) =< s(6588) s(6602) =< s(6589) s(6603) =< s(6592) s(6604) =< s(6603)*s(6582) s(6605) =< s(6604)*s(6582) s(6606) =< s(6591) s(6607) =< s(6606)*aux(367) s(6608) =< s(6607) s(6609) =< s(6578) s(6610) =< s(6603)*s(6582) s(6611) =< s(6610) s(6612) =< s(6593) s(6613) =< s(6612)*s(6579) s(6614) =< s(6613)*s(6579) s(6615) =< s(6595) s(6616) =< s(6594) s(6617) =< s(6596) s(6618) =< s(6597) s(6619) =< s(6618)*s(6579) s(6442) =< aux(344) s(6443) =< aux(344) s(6444) =< aux(344) s(6445) =< aux(344) s(6446) =< aux(344) s(6447) =< aux(344) s(6448) =< aux(344) s(6436) =< aux(344) s(6436) =< aux(346) s(6449) =< aux(347) s(6445) =< aux(348) s(6450) =< aux(350) s(6451) =< aux(351) s(6447) =< aux(352) s(6452) =< aux(353) s(6444) =< aux(353) s(6443) =< aux(354) s(6453) =< aux(345)+1 s(6454) =< aux(345)+3 s(6455) =< aux(345) s(6456) =< aux(345)+2 s(6457) =< aux(345)-1 s(6447) =< aux(346)*(1/5)+aux(352) s(6448) =< aux(346)*(1/5)+aux(352) s(6445) =< aux(346)*(1/3)+aux(348) s(6446) =< aux(346)*(1/3)+aux(348) s(6447) =< aux(346)*(1/3)+aux(348) s(6448) =< aux(346)*(1/3)+aux(348) s(6444) =< aux(346)*(3/7)+aux(353) s(6445) =< aux(346)*(3/7)+aux(353) s(6446) =< aux(346)*(3/7)+aux(353) s(6447) =< aux(346)*(3/7)+aux(353) s(6448) =< aux(346)*(3/7)+aux(353) s(6452) =< aux(346)*(3/7)+aux(353) s(6443) =< aux(346)*(5/9)+s(6436)*(1/9)+aux(354) s(6444) =< aux(346)*(5/9)+s(6436)*(1/9)+aux(354) s(6445) =< aux(346)*(5/9)+s(6436)*(1/9)+aux(354) s(6446) =< aux(346)*(5/9)+s(6436)*(1/9)+aux(354) s(6447) =< aux(346)*(5/9)+s(6436)*(1/9)+aux(354) s(6448) =< aux(346)*(5/9)+s(6436)*(1/9)+aux(354) s(6450) =< aux(346)*(1/5)+aux(350) s(6442) =< aux(346)*(1/5)+aux(350) s(6449) =< aux(346)*(1/4)+aux(347) s(6450) =< aux(346)*(1/4)+aux(347) s(6442) =< aux(346)*(1/4)+aux(347) s(6451) =< aux(346)*(5/16)+aux(351) s(6449) =< aux(346)*(5/16)+aux(351) s(6450) =< aux(346)*(5/16)+aux(351) s(6442) =< aux(346)*(5/16)+aux(351) s(6458) =< s(6448)*s(6453) s(6459) =< s(6448)*s(6453) s(6460) =< s(6448)*s(6454) s(6461) =< s(6447)*s(6454) s(6462) =< s(6445)*s(6455) s(6463) =< s(6445)*s(6456) s(6464) =< s(6445)*s(6455) s(6465) =< s(6444)*s(6455) s(6466) =< s(6444)*s(6456) s(6467) =< s(6443)*s(6453) s(6468) =< s(6450)*s(6457) s(6469) =< s(6450)*s(6455) s(6470) =< s(6449)*s(6455) s(6471) =< s(6451)*s(6453) s(6472) =< s(6459) s(6473) =< s(6460) s(6474) =< s(6461) s(6475) =< s(6462) s(6476) =< s(6463) s(6477) =< s(6466) s(6478) =< s(6477)*s(6456) s(6479) =< s(6478)*s(6456) s(6480) =< s(6465) s(6481) =< s(6480)*aux(345) s(6482) =< s(6481) s(6483) =< s(6452) s(6484) =< s(6477)*s(6456) s(6485) =< s(6484) s(6486) =< s(6467) s(6487) =< s(6486)*s(6453) s(6488) =< s(6487)*s(6453) s(6489) =< s(6469) s(6490) =< s(6468) s(6491) =< s(6470) s(6492) =< s(6471) s(6493) =< s(6492)*s(6453) s(6950) =< s(6948) s(6622) =< aux(356) s(6505) =< aux(355) s(6506) =< aux(355) s(6507) =< aux(355) s(6508) =< aux(355) s(6509) =< aux(355) s(6510) =< aux(355) s(6511) =< aux(355) s(6499) =< aux(355) s(6499) =< aux(357) s(6512) =< aux(358) s(6508) =< aux(359) s(6513) =< aux(361) s(6514) =< aux(362) s(6510) =< aux(363) s(6515) =< aux(364) s(6507) =< aux(364) s(6506) =< aux(365) s(6516) =< aux(356)+1 s(6517) =< aux(356)+3 s(6518) =< aux(356) s(6519) =< aux(356)+2 s(6520) =< aux(356)-1 s(6510) =< aux(357)*(1/5)+aux(363) s(6511) =< aux(357)*(1/5)+aux(363) s(6508) =< aux(357)*(1/3)+aux(359) s(6509) =< aux(357)*(1/3)+aux(359) s(6510) =< aux(357)*(1/3)+aux(359) s(6511) =< aux(357)*(1/3)+aux(359) s(6507) =< aux(357)*(3/7)+aux(364) s(6508) =< aux(357)*(3/7)+aux(364) s(6509) =< aux(357)*(3/7)+aux(364) s(6510) =< aux(357)*(3/7)+aux(364) s(6511) =< aux(357)*(3/7)+aux(364) s(6515) =< aux(357)*(3/7)+aux(364) s(6506) =< aux(357)*(5/9)+s(6499)*(1/9)+aux(365) s(6507) =< aux(357)*(5/9)+s(6499)*(1/9)+aux(365) s(6508) =< aux(357)*(5/9)+s(6499)*(1/9)+aux(365) s(6509) =< aux(357)*(5/9)+s(6499)*(1/9)+aux(365) s(6510) =< aux(357)*(5/9)+s(6499)*(1/9)+aux(365) s(6511) =< aux(357)*(5/9)+s(6499)*(1/9)+aux(365) s(6513) =< aux(357)*(1/5)+aux(361) s(6505) =< aux(357)*(1/5)+aux(361) s(6512) =< aux(357)*(1/4)+aux(358) s(6513) =< aux(357)*(1/4)+aux(358) s(6505) =< aux(357)*(1/4)+aux(358) s(6514) =< aux(357)*(5/16)+aux(362) s(6512) =< aux(357)*(5/16)+aux(362) s(6513) =< aux(357)*(5/16)+aux(362) s(6505) =< aux(357)*(5/16)+aux(362) s(6521) =< s(6511)*s(6516) s(6522) =< s(6511)*s(6516) s(6523) =< s(6511)*s(6517) s(6524) =< s(6510)*s(6517) s(6525) =< s(6508)*s(6518) s(6526) =< s(6508)*s(6519) s(6527) =< s(6508)*s(6518) s(6528) =< s(6507)*s(6518) s(6529) =< s(6507)*s(6519) s(6530) =< s(6506)*s(6516) s(6531) =< s(6513)*s(6520) s(6532) =< s(6513)*s(6518) s(6533) =< s(6512)*s(6518) s(6534) =< s(6514)*s(6516) s(6535) =< s(6522) s(6536) =< s(6523) s(6537) =< s(6524) s(6538) =< s(6525) s(6539) =< s(6526) s(6540) =< s(6529) s(6541) =< s(6540)*s(6519) s(6542) =< s(6541)*s(6519) s(6543) =< s(6528) s(6544) =< s(6543)*aux(356) s(6545) =< s(6544) s(6546) =< s(6515) s(6547) =< s(6540)*s(6519) s(6548) =< s(6547) s(6549) =< s(6530) s(6550) =< s(6549)*s(6516) s(6551) =< s(6550)*s(6516) s(6552) =< s(6532) s(6553) =< s(6531) s(6554) =< s(6533) s(6555) =< s(6534) s(6556) =< s(6555)*s(6516) with precondition: [Out=1,V1>=1,V>=1,V2>=0] * Chain [73]: 5*s(7029)+25*s(7030)+40*s(7031)+30*s(7032)+5*s(7033)+15*s(7034)+15*s(7035)+20*s(7036)+20*s(7037)+20*s(7038)+5*s(7045)+5*s(7051)+10*s(7059)+10*s(7060)+40*s(7061)+15*s(7062)+10*s(7063)+115*s(7064)+20*s(7065)+5*s(7066)+30*s(7067)+30*s(7069)+10*s(7070)+30*s(7072)+60*s(7073)+15*s(7074)+5*s(7075)+10*s(7076)+10*s(7077)+40*s(7078)+35*s(7079)+5*s(7080)+3*s(7092)+15*s(7093)+24*s(7094)+18*s(7095)+3*s(7096)+9*s(7097)+9*s(7098)+12*s(7099)+12*s(7100)+12*s(7101)+3*s(7108)+3*s(7114)+6*s(7122)+6*s(7123)+24*s(7124)+9*s(7125)+6*s(7126)+69*s(7127)+12*s(7128)+3*s(7129)+18*s(7130)+18*s(7132)+6*s(7133)+18*s(7135)+36*s(7136)+9*s(7137)+3*s(7138)+6*s(7139)+6*s(7140)+24*s(7141)+21*s(7142)+3*s(7143)+3*s(7155)+15*s(7156)+24*s(7157)+18*s(7158)+3*s(7159)+9*s(7160)+9*s(7161)+12*s(7162)+12*s(7163)+12*s(7164)+3*s(7171)+3*s(7177)+6*s(7185)+6*s(7186)+24*s(7187)+9*s(7188)+6*s(7189)+69*s(7190)+12*s(7191)+3*s(7192)+18*s(7193)+18*s(7195)+6*s(7196)+18*s(7198)+36*s(7199)+9*s(7200)+3*s(7201)+6*s(7202)+6*s(7203)+24*s(7204)+21*s(7205)+3*s(7206)+23*s(7209)+1*s(7405)+12*s(7664)+4 Such that:aux(380) =< 1 aux(381) =< V1 aux(382) =< 2*V1 aux(383) =< 2*V1+1 aux(384) =< V1/2 aux(385) =< 2/3*V1 aux(386) =< 2/3*V1+1/3 aux(387) =< 3/5*V1 aux(388) =< 3/8*V1 aux(389) =< 4/5*V1 aux(390) =< 4/7*V1 aux(391) =< 4/9*V1 aux(392) =< V aux(393) =< 2*V aux(394) =< 2*V+1 aux(395) =< V/2 aux(396) =< 2/3*V aux(397) =< 2/3*V+1/3 aux(398) =< 3/5*V aux(399) =< 3/8*V aux(400) =< 4/5*V aux(401) =< 4/7*V aux(402) =< 4/9*V aux(403) =< V2 aux(404) =< 2*V2 aux(405) =< 2*V2+1 aux(406) =< V2/2 aux(407) =< 2/3*V2 aux(408) =< 2/3*V2+1/3 aux(409) =< 3/5*V2 aux(410) =< 3/8*V2 aux(411) =< 4/5*V2 aux(412) =< 4/7*V2 aux(413) =< 4/9*V2 s(7023) =< aux(386) s(7086) =< aux(397) s(7149) =< aux(408) s(7664) =< aux(380) s(7155) =< aux(403) s(7156) =< aux(403) s(7157) =< aux(403) s(7158) =< aux(403) s(7159) =< aux(403) s(7160) =< aux(403) s(7161) =< aux(403) s(7149) =< aux(403) s(7149) =< aux(405) s(7162) =< aux(406) s(7158) =< aux(407) s(7163) =< aux(409) s(7164) =< aux(410) s(7160) =< aux(411) s(7165) =< aux(412) s(7157) =< aux(412) s(7156) =< aux(413) s(7166) =< aux(404)+1 s(7167) =< aux(404)+3 s(7168) =< aux(404) s(7169) =< aux(404)+2 s(7170) =< aux(404)-1 s(7160) =< aux(405)*(1/5)+aux(411) s(7161) =< aux(405)*(1/5)+aux(411) s(7158) =< aux(405)*(1/3)+aux(407) s(7159) =< aux(405)*(1/3)+aux(407) s(7160) =< aux(405)*(1/3)+aux(407) s(7161) =< aux(405)*(1/3)+aux(407) s(7157) =< aux(405)*(3/7)+aux(412) s(7158) =< aux(405)*(3/7)+aux(412) s(7159) =< aux(405)*(3/7)+aux(412) s(7160) =< aux(405)*(3/7)+aux(412) s(7161) =< aux(405)*(3/7)+aux(412) s(7165) =< aux(405)*(3/7)+aux(412) s(7156) =< aux(405)*(5/9)+s(7149)*(1/9)+aux(413) s(7157) =< aux(405)*(5/9)+s(7149)*(1/9)+aux(413) s(7158) =< aux(405)*(5/9)+s(7149)*(1/9)+aux(413) s(7159) =< aux(405)*(5/9)+s(7149)*(1/9)+aux(413) s(7160) =< aux(405)*(5/9)+s(7149)*(1/9)+aux(413) s(7161) =< aux(405)*(5/9)+s(7149)*(1/9)+aux(413) s(7163) =< aux(405)*(1/5)+aux(409) s(7155) =< aux(405)*(1/5)+aux(409) s(7162) =< aux(405)*(1/4)+aux(406) s(7163) =< aux(405)*(1/4)+aux(406) s(7155) =< aux(405)*(1/4)+aux(406) s(7164) =< aux(405)*(5/16)+aux(410) s(7162) =< aux(405)*(5/16)+aux(410) s(7163) =< aux(405)*(5/16)+aux(410) s(7155) =< aux(405)*(5/16)+aux(410) s(7171) =< s(7161)*s(7166) s(7172) =< s(7161)*s(7166) s(7173) =< s(7161)*s(7167) s(7174) =< s(7160)*s(7167) s(7175) =< s(7158)*s(7168) s(7176) =< s(7158)*s(7169) s(7177) =< s(7158)*s(7168) s(7178) =< s(7157)*s(7168) s(7179) =< s(7157)*s(7169) s(7180) =< s(7156)*s(7166) s(7181) =< s(7163)*s(7170) s(7182) =< s(7163)*s(7168) s(7183) =< s(7162)*s(7168) s(7184) =< s(7164)*s(7166) s(7185) =< s(7172) s(7186) =< s(7173) s(7187) =< s(7174) s(7188) =< s(7175) s(7189) =< s(7176) s(7190) =< s(7179) s(7191) =< s(7190)*s(7169) s(7192) =< s(7191)*s(7169) s(7193) =< s(7178) s(7194) =< s(7193)*aux(404) s(7195) =< s(7194) s(7196) =< s(7165) s(7197) =< s(7190)*s(7169) s(7198) =< s(7197) s(7199) =< s(7180) s(7200) =< s(7199)*s(7166) s(7201) =< s(7200)*s(7166) s(7202) =< s(7182) s(7203) =< s(7181) s(7204) =< s(7183) s(7205) =< s(7184) s(7206) =< s(7205)*s(7166) s(7029) =< aux(381) s(7030) =< aux(381) s(7031) =< aux(381) s(7032) =< aux(381) s(7033) =< aux(381) s(7034) =< aux(381) s(7035) =< aux(381) s(7023) =< aux(381) s(7023) =< aux(383) s(7036) =< aux(384) s(7032) =< aux(385) s(7037) =< aux(387) s(7038) =< aux(388) s(7034) =< aux(389) s(7039) =< aux(390) s(7031) =< aux(390) s(7030) =< aux(391) s(7040) =< aux(382)+1 s(7041) =< aux(382)+3 s(7042) =< aux(382) s(7043) =< aux(382)+2 s(7044) =< aux(382)-1 s(7034) =< aux(383)*(1/5)+aux(389) s(7035) =< aux(383)*(1/5)+aux(389) s(7032) =< aux(383)*(1/3)+aux(385) s(7033) =< aux(383)*(1/3)+aux(385) s(7034) =< aux(383)*(1/3)+aux(385) s(7035) =< aux(383)*(1/3)+aux(385) s(7031) =< aux(383)*(3/7)+aux(390) s(7032) =< aux(383)*(3/7)+aux(390) s(7033) =< aux(383)*(3/7)+aux(390) s(7034) =< aux(383)*(3/7)+aux(390) s(7035) =< aux(383)*(3/7)+aux(390) s(7039) =< aux(383)*(3/7)+aux(390) s(7030) =< aux(383)*(5/9)+s(7023)*(1/9)+aux(391) s(7031) =< aux(383)*(5/9)+s(7023)*(1/9)+aux(391) s(7032) =< aux(383)*(5/9)+s(7023)*(1/9)+aux(391) s(7033) =< aux(383)*(5/9)+s(7023)*(1/9)+aux(391) s(7034) =< aux(383)*(5/9)+s(7023)*(1/9)+aux(391) s(7035) =< aux(383)*(5/9)+s(7023)*(1/9)+aux(391) s(7037) =< aux(383)*(1/5)+aux(387) s(7029) =< aux(383)*(1/5)+aux(387) s(7036) =< aux(383)*(1/4)+aux(384) s(7037) =< aux(383)*(1/4)+aux(384) s(7029) =< aux(383)*(1/4)+aux(384) s(7038) =< aux(383)*(5/16)+aux(388) s(7036) =< aux(383)*(5/16)+aux(388) s(7037) =< aux(383)*(5/16)+aux(388) s(7029) =< aux(383)*(5/16)+aux(388) s(7045) =< s(7035)*s(7040) s(7046) =< s(7035)*s(7040) s(7047) =< s(7035)*s(7041) s(7048) =< s(7034)*s(7041) s(7049) =< s(7032)*s(7042) s(7050) =< s(7032)*s(7043) s(7051) =< s(7032)*s(7042) s(7052) =< s(7031)*s(7042) s(7053) =< s(7031)*s(7043) s(7054) =< s(7030)*s(7040) s(7055) =< s(7037)*s(7044) s(7056) =< s(7037)*s(7042) s(7057) =< s(7036)*s(7042) s(7058) =< s(7038)*s(7040) s(7059) =< s(7046) s(7060) =< s(7047) s(7061) =< s(7048) s(7062) =< s(7049) s(7063) =< s(7050) s(7064) =< s(7053) s(7065) =< s(7064)*s(7043) s(7066) =< s(7065)*s(7043) s(7067) =< s(7052) s(7068) =< s(7067)*aux(382) s(7069) =< s(7068) s(7070) =< s(7039) s(7071) =< s(7064)*s(7043) s(7072) =< s(7071) s(7073) =< s(7054) s(7074) =< s(7073)*s(7040) s(7075) =< s(7074)*s(7040) s(7076) =< s(7056) s(7077) =< s(7055) s(7078) =< s(7057) s(7079) =< s(7058) s(7080) =< s(7079)*s(7040) s(7209) =< aux(393) s(7092) =< aux(392) s(7093) =< aux(392) s(7094) =< aux(392) s(7095) =< aux(392) s(7096) =< aux(392) s(7097) =< aux(392) s(7098) =< aux(392) s(7086) =< aux(392) s(7086) =< aux(394) s(7099) =< aux(395) s(7095) =< aux(396) s(7100) =< aux(398) s(7101) =< aux(399) s(7097) =< aux(400) s(7102) =< aux(401) s(7094) =< aux(401) s(7093) =< aux(402) s(7103) =< aux(393)+1 s(7104) =< aux(393)+3 s(7105) =< aux(393) s(7106) =< aux(393)+2 s(7107) =< aux(393)-1 s(7097) =< aux(394)*(1/5)+aux(400) s(7098) =< aux(394)*(1/5)+aux(400) s(7095) =< aux(394)*(1/3)+aux(396) s(7096) =< aux(394)*(1/3)+aux(396) s(7097) =< aux(394)*(1/3)+aux(396) s(7098) =< aux(394)*(1/3)+aux(396) s(7094) =< aux(394)*(3/7)+aux(401) s(7095) =< aux(394)*(3/7)+aux(401) s(7096) =< aux(394)*(3/7)+aux(401) s(7097) =< aux(394)*(3/7)+aux(401) s(7098) =< aux(394)*(3/7)+aux(401) s(7102) =< aux(394)*(3/7)+aux(401) s(7093) =< aux(394)*(5/9)+s(7086)*(1/9)+aux(402) s(7094) =< aux(394)*(5/9)+s(7086)*(1/9)+aux(402) s(7095) =< aux(394)*(5/9)+s(7086)*(1/9)+aux(402) s(7096) =< aux(394)*(5/9)+s(7086)*(1/9)+aux(402) s(7097) =< aux(394)*(5/9)+s(7086)*(1/9)+aux(402) s(7098) =< aux(394)*(5/9)+s(7086)*(1/9)+aux(402) s(7100) =< aux(394)*(1/5)+aux(398) s(7092) =< aux(394)*(1/5)+aux(398) s(7099) =< aux(394)*(1/4)+aux(395) s(7100) =< aux(394)*(1/4)+aux(395) s(7092) =< aux(394)*(1/4)+aux(395) s(7101) =< aux(394)*(5/16)+aux(399) s(7099) =< aux(394)*(5/16)+aux(399) s(7100) =< aux(394)*(5/16)+aux(399) s(7092) =< aux(394)*(5/16)+aux(399) s(7108) =< s(7098)*s(7103) s(7109) =< s(7098)*s(7103) s(7110) =< s(7098)*s(7104) s(7111) =< s(7097)*s(7104) s(7112) =< s(7095)*s(7105) s(7113) =< s(7095)*s(7106) s(7114) =< s(7095)*s(7105) s(7115) =< s(7094)*s(7105) s(7116) =< s(7094)*s(7106) s(7117) =< s(7093)*s(7103) s(7118) =< s(7100)*s(7107) s(7119) =< s(7100)*s(7105) s(7120) =< s(7099)*s(7105) s(7121) =< s(7101)*s(7103) s(7122) =< s(7109) s(7123) =< s(7110) s(7124) =< s(7111) s(7125) =< s(7112) s(7126) =< s(7113) s(7127) =< s(7116) s(7128) =< s(7127)*s(7106) s(7129) =< s(7128)*s(7106) s(7130) =< s(7115) s(7131) =< s(7130)*aux(393) s(7132) =< s(7131) s(7133) =< s(7102) s(7134) =< s(7127)*s(7106) s(7135) =< s(7134) s(7136) =< s(7117) s(7137) =< s(7136)*s(7103) s(7138) =< s(7137)*s(7103) s(7139) =< s(7119) s(7140) =< s(7118) s(7141) =< s(7120) s(7142) =< s(7121) s(7143) =< s(7142)*s(7103) s(7405) =< s(7209)*aux(393) with precondition: [V1>=1,V2>=0,Out>=2,2*V>=Out] * Chain [72]: 1*s(7744)+5*s(7745)+8*s(7746)+6*s(7747)+1*s(7748)+3*s(7749)+3*s(7750)+4*s(7751)+4*s(7752)+4*s(7753)+1*s(7760)+1*s(7766)+2*s(7774)+2*s(7775)+8*s(7776)+3*s(7777)+2*s(7778)+23*s(7779)+4*s(7780)+1*s(7781)+6*s(7782)+6*s(7784)+2*s(7785)+6*s(7787)+12*s(7788)+3*s(7789)+1*s(7790)+2*s(7791)+2*s(7792)+8*s(7793)+7*s(7794)+1*s(7795)+1*s(7807)+5*s(7808)+8*s(7809)+6*s(7810)+1*s(7811)+3*s(7812)+3*s(7813)+4*s(7814)+4*s(7815)+4*s(7816)+1*s(7823)+1*s(7829)+2*s(7837)+2*s(7838)+8*s(7839)+3*s(7840)+2*s(7841)+23*s(7842)+4*s(7843)+1*s(7844)+6*s(7845)+6*s(7847)+2*s(7848)+6*s(7850)+12*s(7851)+3*s(7852)+1*s(7853)+2*s(7854)+2*s(7855)+8*s(7856)+7*s(7857)+1*s(7858)+2*s(7861)+2*s(7862)+4 Such that:s(7860) =< 2 s(7733) =< V1 s(7734) =< 2*V1 s(7735) =< 2*V1+1 s(7736) =< V1/2 s(7737) =< 2/3*V1 s(7738) =< 2/3*V1+1/3 s(7739) =< 3/5*V1 s(7740) =< 3/8*V1 s(7741) =< 4/5*V1 s(7742) =< 4/7*V1 s(7743) =< 4/9*V1 s(7796) =< V s(7798) =< 2*V+1 s(7799) =< V/2 s(7800) =< 2/3*V s(7801) =< 2/3*V+1/3 s(7802) =< 3/5*V s(7803) =< 3/8*V s(7804) =< 4/5*V s(7805) =< 4/7*V s(7806) =< 4/9*V aux(414) =< 2*V s(7861) =< aux(414) s(7862) =< s(7860) s(7807) =< s(7796) s(7808) =< s(7796) s(7809) =< s(7796) s(7810) =< s(7796) s(7811) =< s(7796) s(7812) =< s(7796) s(7813) =< s(7796) s(7801) =< s(7796) s(7801) =< s(7798) s(7814) =< s(7799) s(7810) =< s(7800) s(7815) =< s(7802) s(7816) =< s(7803) s(7812) =< s(7804) s(7817) =< s(7805) s(7809) =< s(7805) s(7808) =< s(7806) s(7818) =< aux(414)+1 s(7819) =< aux(414)+3 s(7820) =< aux(414) s(7821) =< aux(414)+2 s(7822) =< aux(414)-1 s(7812) =< s(7798)*(1/5)+s(7804) s(7813) =< s(7798)*(1/5)+s(7804) s(7810) =< s(7798)*(1/3)+s(7800) s(7811) =< s(7798)*(1/3)+s(7800) s(7812) =< s(7798)*(1/3)+s(7800) s(7813) =< s(7798)*(1/3)+s(7800) s(7809) =< s(7798)*(3/7)+s(7805) s(7810) =< s(7798)*(3/7)+s(7805) s(7811) =< s(7798)*(3/7)+s(7805) s(7812) =< s(7798)*(3/7)+s(7805) s(7813) =< s(7798)*(3/7)+s(7805) s(7817) =< s(7798)*(3/7)+s(7805) s(7808) =< s(7798)*(5/9)+s(7801)*(1/9)+s(7806) s(7809) =< s(7798)*(5/9)+s(7801)*(1/9)+s(7806) s(7810) =< s(7798)*(5/9)+s(7801)*(1/9)+s(7806) s(7811) =< s(7798)*(5/9)+s(7801)*(1/9)+s(7806) s(7812) =< s(7798)*(5/9)+s(7801)*(1/9)+s(7806) s(7813) =< s(7798)*(5/9)+s(7801)*(1/9)+s(7806) s(7815) =< s(7798)*(1/5)+s(7802) s(7807) =< s(7798)*(1/5)+s(7802) s(7814) =< s(7798)*(1/4)+s(7799) s(7815) =< s(7798)*(1/4)+s(7799) s(7807) =< s(7798)*(1/4)+s(7799) s(7816) =< s(7798)*(5/16)+s(7803) s(7814) =< s(7798)*(5/16)+s(7803) s(7815) =< s(7798)*(5/16)+s(7803) s(7807) =< s(7798)*(5/16)+s(7803) s(7823) =< s(7813)*s(7818) s(7824) =< s(7813)*s(7818) s(7825) =< s(7813)*s(7819) s(7826) =< s(7812)*s(7819) s(7827) =< s(7810)*s(7820) s(7828) =< s(7810)*s(7821) s(7829) =< s(7810)*s(7820) s(7830) =< s(7809)*s(7820) s(7831) =< s(7809)*s(7821) s(7832) =< s(7808)*s(7818) s(7833) =< s(7815)*s(7822) s(7834) =< s(7815)*s(7820) s(7835) =< s(7814)*s(7820) s(7836) =< s(7816)*s(7818) s(7837) =< s(7824) s(7838) =< s(7825) s(7839) =< s(7826) s(7840) =< s(7827) s(7841) =< s(7828) s(7842) =< s(7831) s(7843) =< s(7842)*s(7821) s(7844) =< s(7843)*s(7821) s(7845) =< s(7830) s(7846) =< s(7845)*aux(414) s(7847) =< s(7846) s(7848) =< s(7817) s(7849) =< s(7842)*s(7821) s(7850) =< s(7849) s(7851) =< s(7832) s(7852) =< s(7851)*s(7818) s(7853) =< s(7852)*s(7818) s(7854) =< s(7834) s(7855) =< s(7833) s(7856) =< s(7835) s(7857) =< s(7836) s(7858) =< s(7857)*s(7818) s(7744) =< s(7733) s(7745) =< s(7733) s(7746) =< s(7733) s(7747) =< s(7733) s(7748) =< s(7733) s(7749) =< s(7733) s(7750) =< s(7733) s(7738) =< s(7733) s(7738) =< s(7735) s(7751) =< s(7736) s(7747) =< s(7737) s(7752) =< s(7739) s(7753) =< s(7740) s(7749) =< s(7741) s(7754) =< s(7742) s(7746) =< s(7742) s(7745) =< s(7743) s(7755) =< s(7734)+1 s(7756) =< s(7734)+3 s(7757) =< s(7734) s(7758) =< s(7734)+2 s(7759) =< s(7734)-1 s(7749) =< s(7735)*(1/5)+s(7741) s(7750) =< s(7735)*(1/5)+s(7741) s(7747) =< s(7735)*(1/3)+s(7737) s(7748) =< s(7735)*(1/3)+s(7737) s(7749) =< s(7735)*(1/3)+s(7737) s(7750) =< s(7735)*(1/3)+s(7737) s(7746) =< s(7735)*(3/7)+s(7742) s(7747) =< s(7735)*(3/7)+s(7742) s(7748) =< s(7735)*(3/7)+s(7742) s(7749) =< s(7735)*(3/7)+s(7742) s(7750) =< s(7735)*(3/7)+s(7742) s(7754) =< s(7735)*(3/7)+s(7742) s(7745) =< s(7735)*(5/9)+s(7738)*(1/9)+s(7743) s(7746) =< s(7735)*(5/9)+s(7738)*(1/9)+s(7743) s(7747) =< s(7735)*(5/9)+s(7738)*(1/9)+s(7743) s(7748) =< s(7735)*(5/9)+s(7738)*(1/9)+s(7743) s(7749) =< s(7735)*(5/9)+s(7738)*(1/9)+s(7743) s(7750) =< s(7735)*(5/9)+s(7738)*(1/9)+s(7743) s(7752) =< s(7735)*(1/5)+s(7739) s(7744) =< s(7735)*(1/5)+s(7739) s(7751) =< s(7735)*(1/4)+s(7736) s(7752) =< s(7735)*(1/4)+s(7736) s(7744) =< s(7735)*(1/4)+s(7736) s(7753) =< s(7735)*(5/16)+s(7740) s(7751) =< s(7735)*(5/16)+s(7740) s(7752) =< s(7735)*(5/16)+s(7740) s(7744) =< s(7735)*(5/16)+s(7740) s(7760) =< s(7750)*s(7755) s(7761) =< s(7750)*s(7755) s(7762) =< s(7750)*s(7756) s(7763) =< s(7749)*s(7756) s(7764) =< s(7747)*s(7757) s(7765) =< s(7747)*s(7758) s(7766) =< s(7747)*s(7757) s(7767) =< s(7746)*s(7757) s(7768) =< s(7746)*s(7758) s(7769) =< s(7745)*s(7755) s(7770) =< s(7752)*s(7759) s(7771) =< s(7752)*s(7757) s(7772) =< s(7751)*s(7757) s(7773) =< s(7753)*s(7755) s(7774) =< s(7761) s(7775) =< s(7762) s(7776) =< s(7763) s(7777) =< s(7764) s(7778) =< s(7765) s(7779) =< s(7768) s(7780) =< s(7779)*s(7758) s(7781) =< s(7780)*s(7758) s(7782) =< s(7767) s(7783) =< s(7782)*s(7734) s(7784) =< s(7783) s(7785) =< s(7754) s(7786) =< s(7779)*s(7758) s(7787) =< s(7786) s(7788) =< s(7769) s(7789) =< s(7788)*s(7755) s(7790) =< s(7789)*s(7755) s(7791) =< s(7771) s(7792) =< s(7770) s(7793) =< s(7772) s(7794) =< s(7773) s(7795) =< s(7794)*s(7755) with precondition: [V2=2,Out=1,V1>=1,V>=1] * Chain [71]: 1*s(7874)+5*s(7875)+8*s(7876)+6*s(7877)+1*s(7878)+3*s(7879)+3*s(7880)+4*s(7881)+4*s(7882)+4*s(7883)+1*s(7890)+1*s(7896)+2*s(7904)+2*s(7905)+8*s(7906)+3*s(7907)+2*s(7908)+23*s(7909)+4*s(7910)+1*s(7911)+6*s(7912)+6*s(7914)+2*s(7915)+6*s(7917)+12*s(7918)+3*s(7919)+1*s(7920)+2*s(7921)+2*s(7922)+8*s(7923)+7*s(7924)+1*s(7925)+1*s(7937)+5*s(7938)+8*s(7939)+6*s(7940)+1*s(7941)+3*s(7942)+3*s(7943)+4*s(7944)+4*s(7945)+4*s(7946)+1*s(7953)+1*s(7959)+2*s(7967)+2*s(7968)+8*s(7969)+3*s(7970)+2*s(7971)+23*s(7972)+4*s(7973)+1*s(7974)+6*s(7975)+6*s(7977)+2*s(7978)+6*s(7980)+12*s(7981)+3*s(7982)+1*s(7983)+2*s(7984)+2*s(7985)+8*s(7986)+7*s(7987)+1*s(7988)+5*s(7990)+2*s(7993)+1*s(7994)+4 Such that:s(7991) =< 2 s(7863) =< V1 s(7864) =< 2*V1 s(7865) =< 2*V1+1 s(7866) =< V1/2 s(7867) =< 2/3*V1 s(7868) =< 2/3*V1+1/3 s(7869) =< 3/5*V1 s(7870) =< 3/8*V1 s(7871) =< 4/5*V1 s(7872) =< 4/7*V1 s(7873) =< 4/9*V1 s(7926) =< V s(7928) =< 2*V+1 s(7929) =< V/2 s(7930) =< 2/3*V s(7931) =< 2/3*V+1/3 s(7932) =< 3/5*V s(7933) =< 3/8*V s(7934) =< 4/5*V s(7935) =< 4/7*V s(7936) =< 4/9*V aux(415) =< 2*V s(7990) =< aux(415) s(7993) =< s(7991) s(7994) =< s(7990)*s(7991) s(7937) =< s(7926) s(7938) =< s(7926) s(7939) =< s(7926) s(7940) =< s(7926) s(7941) =< s(7926) s(7942) =< s(7926) s(7943) =< s(7926) s(7931) =< s(7926) s(7931) =< s(7928) s(7944) =< s(7929) s(7940) =< s(7930) s(7945) =< s(7932) s(7946) =< s(7933) s(7942) =< s(7934) s(7947) =< s(7935) s(7939) =< s(7935) s(7938) =< s(7936) s(7948) =< aux(415)+1 s(7949) =< aux(415)+3 s(7950) =< aux(415) s(7951) =< aux(415)+2 s(7952) =< aux(415)-1 s(7942) =< s(7928)*(1/5)+s(7934) s(7943) =< s(7928)*(1/5)+s(7934) s(7940) =< s(7928)*(1/3)+s(7930) s(7941) =< s(7928)*(1/3)+s(7930) s(7942) =< s(7928)*(1/3)+s(7930) s(7943) =< s(7928)*(1/3)+s(7930) s(7939) =< s(7928)*(3/7)+s(7935) s(7940) =< s(7928)*(3/7)+s(7935) s(7941) =< s(7928)*(3/7)+s(7935) s(7942) =< s(7928)*(3/7)+s(7935) s(7943) =< s(7928)*(3/7)+s(7935) s(7947) =< s(7928)*(3/7)+s(7935) s(7938) =< s(7928)*(5/9)+s(7931)*(1/9)+s(7936) s(7939) =< s(7928)*(5/9)+s(7931)*(1/9)+s(7936) s(7940) =< s(7928)*(5/9)+s(7931)*(1/9)+s(7936) s(7941) =< s(7928)*(5/9)+s(7931)*(1/9)+s(7936) s(7942) =< s(7928)*(5/9)+s(7931)*(1/9)+s(7936) s(7943) =< s(7928)*(5/9)+s(7931)*(1/9)+s(7936) s(7945) =< s(7928)*(1/5)+s(7932) s(7937) =< s(7928)*(1/5)+s(7932) s(7944) =< s(7928)*(1/4)+s(7929) s(7945) =< s(7928)*(1/4)+s(7929) s(7937) =< s(7928)*(1/4)+s(7929) s(7946) =< s(7928)*(5/16)+s(7933) s(7944) =< s(7928)*(5/16)+s(7933) s(7945) =< s(7928)*(5/16)+s(7933) s(7937) =< s(7928)*(5/16)+s(7933) s(7953) =< s(7943)*s(7948) s(7954) =< s(7943)*s(7948) s(7955) =< s(7943)*s(7949) s(7956) =< s(7942)*s(7949) s(7957) =< s(7940)*s(7950) s(7958) =< s(7940)*s(7951) s(7959) =< s(7940)*s(7950) s(7960) =< s(7939)*s(7950) s(7961) =< s(7939)*s(7951) s(7962) =< s(7938)*s(7948) s(7963) =< s(7945)*s(7952) s(7964) =< s(7945)*s(7950) s(7965) =< s(7944)*s(7950) s(7966) =< s(7946)*s(7948) s(7967) =< s(7954) s(7968) =< s(7955) s(7969) =< s(7956) s(7970) =< s(7957) s(7971) =< s(7958) s(7972) =< s(7961) s(7973) =< s(7972)*s(7951) s(7974) =< s(7973)*s(7951) s(7975) =< s(7960) s(7976) =< s(7975)*aux(415) s(7977) =< s(7976) s(7978) =< s(7947) s(7979) =< s(7972)*s(7951) s(7980) =< s(7979) s(7981) =< s(7962) s(7982) =< s(7981)*s(7948) s(7983) =< s(7982)*s(7948) s(7984) =< s(7964) s(7985) =< s(7963) s(7986) =< s(7965) s(7987) =< s(7966) s(7988) =< s(7987)*s(7948) s(7874) =< s(7863) s(7875) =< s(7863) s(7876) =< s(7863) s(7877) =< s(7863) s(7878) =< s(7863) s(7879) =< s(7863) s(7880) =< s(7863) s(7868) =< s(7863) s(7868) =< s(7865) s(7881) =< s(7866) s(7877) =< s(7867) s(7882) =< s(7869) s(7883) =< s(7870) s(7879) =< s(7871) s(7884) =< s(7872) s(7876) =< s(7872) s(7875) =< s(7873) s(7885) =< s(7864)+1 s(7886) =< s(7864)+3 s(7887) =< s(7864) s(7888) =< s(7864)+2 s(7889) =< s(7864)-1 s(7879) =< s(7865)*(1/5)+s(7871) s(7880) =< s(7865)*(1/5)+s(7871) s(7877) =< s(7865)*(1/3)+s(7867) s(7878) =< s(7865)*(1/3)+s(7867) s(7879) =< s(7865)*(1/3)+s(7867) s(7880) =< s(7865)*(1/3)+s(7867) s(7876) =< s(7865)*(3/7)+s(7872) s(7877) =< s(7865)*(3/7)+s(7872) s(7878) =< s(7865)*(3/7)+s(7872) s(7879) =< s(7865)*(3/7)+s(7872) s(7880) =< s(7865)*(3/7)+s(7872) s(7884) =< s(7865)*(3/7)+s(7872) s(7875) =< s(7865)*(5/9)+s(7868)*(1/9)+s(7873) s(7876) =< s(7865)*(5/9)+s(7868)*(1/9)+s(7873) s(7877) =< s(7865)*(5/9)+s(7868)*(1/9)+s(7873) s(7878) =< s(7865)*(5/9)+s(7868)*(1/9)+s(7873) s(7879) =< s(7865)*(5/9)+s(7868)*(1/9)+s(7873) s(7880) =< s(7865)*(5/9)+s(7868)*(1/9)+s(7873) s(7882) =< s(7865)*(1/5)+s(7869) s(7874) =< s(7865)*(1/5)+s(7869) s(7881) =< s(7865)*(1/4)+s(7866) s(7882) =< s(7865)*(1/4)+s(7866) s(7874) =< s(7865)*(1/4)+s(7866) s(7883) =< s(7865)*(5/16)+s(7870) s(7881) =< s(7865)*(5/16)+s(7870) s(7882) =< s(7865)*(5/16)+s(7870) s(7874) =< s(7865)*(5/16)+s(7870) s(7890) =< s(7880)*s(7885) s(7891) =< s(7880)*s(7885) s(7892) =< s(7880)*s(7886) s(7893) =< s(7879)*s(7886) s(7894) =< s(7877)*s(7887) s(7895) =< s(7877)*s(7888) s(7896) =< s(7877)*s(7887) s(7897) =< s(7876)*s(7887) s(7898) =< s(7876)*s(7888) s(7899) =< s(7875)*s(7885) s(7900) =< s(7882)*s(7889) s(7901) =< s(7882)*s(7887) s(7902) =< s(7881)*s(7887) s(7903) =< s(7883)*s(7885) s(7904) =< s(7891) s(7905) =< s(7892) s(7906) =< s(7893) s(7907) =< s(7894) s(7908) =< s(7895) s(7909) =< s(7898) s(7910) =< s(7909)*s(7888) s(7911) =< s(7910)*s(7888) s(7912) =< s(7897) s(7913) =< s(7912)*s(7864) s(7914) =< s(7913) s(7915) =< s(7884) s(7916) =< s(7909)*s(7888) s(7917) =< s(7916) s(7918) =< s(7899) s(7919) =< s(7918)*s(7885) s(7920) =< s(7919)*s(7885) s(7921) =< s(7901) s(7922) =< s(7900) s(7923) =< s(7902) s(7924) =< s(7903) s(7925) =< s(7924)*s(7885) with precondition: [V2=2,V1>=1,Out>=2,2*V>=Out+2] #### Cost of chains of fun7(V1,V,Out): * Chain [84]: 2*s(8979)+10*s(8980)+16*s(8981)+12*s(8982)+2*s(8983)+6*s(8984)+6*s(8985)+8*s(8986)+8*s(8987)+8*s(8988)+2*s(8995)+2*s(9001)+4*s(9009)+4*s(9010)+16*s(9011)+6*s(9012)+4*s(9013)+46*s(9014)+8*s(9015)+2*s(9016)+12*s(9017)+12*s(9019)+4*s(9020)+12*s(9022)+24*s(9023)+6*s(9024)+2*s(9025)+4*s(9026)+4*s(9027)+16*s(9028)+14*s(9029)+2*s(9030)+3*s(9042)+15*s(9043)+24*s(9044)+18*s(9045)+3*s(9046)+9*s(9047)+9*s(9048)+12*s(9049)+12*s(9050)+12*s(9051)+3*s(9058)+3*s(9064)+6*s(9072)+6*s(9073)+24*s(9074)+9*s(9075)+6*s(9076)+69*s(9077)+12*s(9078)+3*s(9079)+18*s(9080)+18*s(9082)+6*s(9083)+18*s(9085)+36*s(9086)+9*s(9087)+3*s(9088)+6*s(9089)+6*s(9090)+24*s(9091)+21*s(9092)+3*s(9093)+1 Such that:aux(483) =< V1 aux(484) =< 2*V1 aux(485) =< 2*V1+1 aux(486) =< V1/2 aux(487) =< 2/3*V1 aux(488) =< 2/3*V1+1/3 aux(489) =< 3/5*V1 aux(490) =< 3/8*V1 aux(491) =< 4/5*V1 aux(492) =< 4/7*V1 aux(493) =< 4/9*V1 aux(494) =< V aux(495) =< 2*V aux(496) =< 2*V+1 aux(497) =< V/2 aux(498) =< 2/3*V aux(499) =< 2/3*V+1/3 aux(500) =< 3/5*V aux(501) =< 3/8*V aux(502) =< 4/5*V aux(503) =< 4/7*V aux(504) =< 4/9*V s(8973) =< aux(488) s(9036) =< aux(499) s(9042) =< aux(494) s(9043) =< aux(494) s(9044) =< aux(494) s(9045) =< aux(494) s(9046) =< aux(494) s(9047) =< aux(494) s(9048) =< aux(494) s(9036) =< aux(494) s(9036) =< aux(496) s(9049) =< aux(497) s(9045) =< aux(498) s(9050) =< aux(500) s(9051) =< aux(501) s(9047) =< aux(502) s(9052) =< aux(503) s(9044) =< aux(503) s(9043) =< aux(504) s(9053) =< aux(495)+1 s(9054) =< aux(495)+3 s(9055) =< aux(495) s(9056) =< aux(495)+2 s(9057) =< aux(495)-1 s(9047) =< aux(496)*(1/5)+aux(502) s(9048) =< aux(496)*(1/5)+aux(502) s(9045) =< aux(496)*(1/3)+aux(498) s(9046) =< aux(496)*(1/3)+aux(498) s(9047) =< aux(496)*(1/3)+aux(498) s(9048) =< aux(496)*(1/3)+aux(498) s(9044) =< aux(496)*(3/7)+aux(503) s(9045) =< aux(496)*(3/7)+aux(503) s(9046) =< aux(496)*(3/7)+aux(503) s(9047) =< aux(496)*(3/7)+aux(503) s(9048) =< aux(496)*(3/7)+aux(503) s(9052) =< aux(496)*(3/7)+aux(503) s(9043) =< aux(496)*(5/9)+s(9036)*(1/9)+aux(504) s(9044) =< aux(496)*(5/9)+s(9036)*(1/9)+aux(504) s(9045) =< aux(496)*(5/9)+s(9036)*(1/9)+aux(504) s(9046) =< aux(496)*(5/9)+s(9036)*(1/9)+aux(504) s(9047) =< aux(496)*(5/9)+s(9036)*(1/9)+aux(504) s(9048) =< aux(496)*(5/9)+s(9036)*(1/9)+aux(504) s(9050) =< aux(496)*(1/5)+aux(500) s(9042) =< aux(496)*(1/5)+aux(500) s(9049) =< aux(496)*(1/4)+aux(497) s(9050) =< aux(496)*(1/4)+aux(497) s(9042) =< aux(496)*(1/4)+aux(497) s(9051) =< aux(496)*(5/16)+aux(501) s(9049) =< aux(496)*(5/16)+aux(501) s(9050) =< aux(496)*(5/16)+aux(501) s(9042) =< aux(496)*(5/16)+aux(501) s(9058) =< s(9048)*s(9053) s(9059) =< s(9048)*s(9053) s(9060) =< s(9048)*s(9054) s(9061) =< s(9047)*s(9054) s(9062) =< s(9045)*s(9055) s(9063) =< s(9045)*s(9056) s(9064) =< s(9045)*s(9055) s(9065) =< s(9044)*s(9055) s(9066) =< s(9044)*s(9056) s(9067) =< s(9043)*s(9053) s(9068) =< s(9050)*s(9057) s(9069) =< s(9050)*s(9055) s(9070) =< s(9049)*s(9055) s(9071) =< s(9051)*s(9053) s(9072) =< s(9059) s(9073) =< s(9060) s(9074) =< s(9061) s(9075) =< s(9062) s(9076) =< s(9063) s(9077) =< s(9066) s(9078) =< s(9077)*s(9056) s(9079) =< s(9078)*s(9056) s(9080) =< s(9065) s(9081) =< s(9080)*aux(495) s(9082) =< s(9081) s(9083) =< s(9052) s(9084) =< s(9077)*s(9056) s(9085) =< s(9084) s(9086) =< s(9067) s(9087) =< s(9086)*s(9053) s(9088) =< s(9087)*s(9053) s(9089) =< s(9069) s(9090) =< s(9068) s(9091) =< s(9070) s(9092) =< s(9071) s(9093) =< s(9092)*s(9053) s(8979) =< aux(483) s(8980) =< aux(483) s(8981) =< aux(483) s(8982) =< aux(483) s(8983) =< aux(483) s(8984) =< aux(483) s(8985) =< aux(483) s(8973) =< aux(483) s(8973) =< aux(485) s(8986) =< aux(486) s(8982) =< aux(487) s(8987) =< aux(489) s(8988) =< aux(490) s(8984) =< aux(491) s(8989) =< aux(492) s(8981) =< aux(492) s(8980) =< aux(493) s(8990) =< aux(484)+1 s(8991) =< aux(484)+3 s(8992) =< aux(484) s(8993) =< aux(484)+2 s(8994) =< aux(484)-1 s(8984) =< aux(485)*(1/5)+aux(491) s(8985) =< aux(485)*(1/5)+aux(491) s(8982) =< aux(485)*(1/3)+aux(487) s(8983) =< aux(485)*(1/3)+aux(487) s(8984) =< aux(485)*(1/3)+aux(487) s(8985) =< aux(485)*(1/3)+aux(487) s(8981) =< aux(485)*(3/7)+aux(492) s(8982) =< aux(485)*(3/7)+aux(492) s(8983) =< aux(485)*(3/7)+aux(492) s(8984) =< aux(485)*(3/7)+aux(492) s(8985) =< aux(485)*(3/7)+aux(492) s(8989) =< aux(485)*(3/7)+aux(492) s(8980) =< aux(485)*(5/9)+s(8973)*(1/9)+aux(493) s(8981) =< aux(485)*(5/9)+s(8973)*(1/9)+aux(493) s(8982) =< aux(485)*(5/9)+s(8973)*(1/9)+aux(493) s(8983) =< aux(485)*(5/9)+s(8973)*(1/9)+aux(493) s(8984) =< aux(485)*(5/9)+s(8973)*(1/9)+aux(493) s(8985) =< aux(485)*(5/9)+s(8973)*(1/9)+aux(493) s(8987) =< aux(485)*(1/5)+aux(489) s(8979) =< aux(485)*(1/5)+aux(489) s(8986) =< aux(485)*(1/4)+aux(486) s(8987) =< aux(485)*(1/4)+aux(486) s(8979) =< aux(485)*(1/4)+aux(486) s(8988) =< aux(485)*(5/16)+aux(490) s(8986) =< aux(485)*(5/16)+aux(490) s(8987) =< aux(485)*(5/16)+aux(490) s(8979) =< aux(485)*(5/16)+aux(490) s(8995) =< s(8985)*s(8990) s(8996) =< s(8985)*s(8990) s(8997) =< s(8985)*s(8991) s(8998) =< s(8984)*s(8991) s(8999) =< s(8982)*s(8992) s(9000) =< s(8982)*s(8993) s(9001) =< s(8982)*s(8992) s(9002) =< s(8981)*s(8992) s(9003) =< s(8981)*s(8993) s(9004) =< s(8980)*s(8990) s(9005) =< s(8987)*s(8994) s(9006) =< s(8987)*s(8992) s(9007) =< s(8986)*s(8992) s(9008) =< s(8988)*s(8990) s(9009) =< s(8996) s(9010) =< s(8997) s(9011) =< s(8998) s(9012) =< s(8999) s(9013) =< s(9000) s(9014) =< s(9003) s(9015) =< s(9014)*s(8993) s(9016) =< s(9015)*s(8993) s(9017) =< s(9002) s(9018) =< s(9017)*aux(484) s(9019) =< s(9018) s(9020) =< s(8989) s(9021) =< s(9014)*s(8993) s(9022) =< s(9021) s(9023) =< s(9004) s(9024) =< s(9023)*s(8990) s(9025) =< s(9024)*s(8990) s(9026) =< s(9006) s(9027) =< s(9005) s(9028) =< s(9007) s(9029) =< s(9008) s(9030) =< s(9029)*s(8990) with precondition: [Out=0,V1>=0,V>=0] * Chain [83]: 3*s(9294)+15*s(9295)+24*s(9296)+18*s(9297)+3*s(9298)+9*s(9299)+9*s(9300)+12*s(9301)+12*s(9302)+12*s(9303)+3*s(9310)+3*s(9316)+6*s(9324)+6*s(9325)+24*s(9326)+9*s(9327)+6*s(9328)+69*s(9329)+12*s(9330)+3*s(9331)+18*s(9332)+18*s(9334)+6*s(9335)+18*s(9337)+36*s(9338)+9*s(9339)+3*s(9340)+6*s(9341)+6*s(9342)+24*s(9343)+21*s(9344)+3*s(9345)+5*s(9357)+25*s(9358)+40*s(9359)+30*s(9360)+5*s(9361)+15*s(9362)+15*s(9363)+20*s(9364)+20*s(9365)+20*s(9366)+5*s(9373)+5*s(9379)+10*s(9387)+10*s(9388)+40*s(9389)+15*s(9390)+10*s(9391)+115*s(9392)+20*s(9393)+5*s(9394)+30*s(9395)+30*s(9397)+10*s(9398)+30*s(9400)+60*s(9401)+15*s(9402)+5*s(9403)+10*s(9404)+10*s(9405)+40*s(9406)+35*s(9407)+5*s(9408)+16*s(9410)+6*s(9412)+4*s(9542)+3*s(9676)+4*s(9677)+1*s(9678)+12*s(9743)+6*s(9745)+5 Such that:aux(512) =< 2 aux(513) =< V1 aux(514) =< 2*V1 aux(515) =< 2*V1+1 aux(516) =< V1/2 aux(517) =< 2/3*V1 aux(518) =< 2/3*V1+1/3 aux(519) =< 3/5*V1 aux(520) =< 3/8*V1 aux(521) =< 4/5*V1 aux(522) =< 4/7*V1 aux(523) =< 4/9*V1 aux(524) =< V aux(525) =< 2*V aux(526) =< 2*V+1 aux(527) =< V/2 aux(528) =< 2/3*V aux(529) =< 2/3*V+1/3 aux(530) =< 3/5*V aux(531) =< 3/8*V aux(532) =< 4/5*V aux(533) =< 4/7*V aux(534) =< 4/9*V s(9288) =< aux(518) s(9351) =< aux(529) s(9743) =< aux(512) s(9744) =< s(9743)*aux(512) s(9745) =< s(9744) s(9357) =< aux(524) s(9358) =< aux(524) s(9359) =< aux(524) s(9360) =< aux(524) s(9361) =< aux(524) s(9362) =< aux(524) s(9363) =< aux(524) s(9351) =< aux(524) s(9351) =< aux(526) s(9364) =< aux(527) s(9360) =< aux(528) s(9365) =< aux(530) s(9366) =< aux(531) s(9362) =< aux(532) s(9367) =< aux(533) s(9359) =< aux(533) s(9358) =< aux(534) s(9368) =< aux(525)+1 s(9369) =< aux(525)+3 s(9370) =< aux(525) s(9371) =< aux(525)+2 s(9372) =< aux(525)-1 s(9362) =< aux(526)*(1/5)+aux(532) s(9363) =< aux(526)*(1/5)+aux(532) s(9360) =< aux(526)*(1/3)+aux(528) s(9361) =< aux(526)*(1/3)+aux(528) s(9362) =< aux(526)*(1/3)+aux(528) s(9363) =< aux(526)*(1/3)+aux(528) s(9359) =< aux(526)*(3/7)+aux(533) s(9360) =< aux(526)*(3/7)+aux(533) s(9361) =< aux(526)*(3/7)+aux(533) s(9362) =< aux(526)*(3/7)+aux(533) s(9363) =< aux(526)*(3/7)+aux(533) s(9367) =< aux(526)*(3/7)+aux(533) s(9358) =< aux(526)*(5/9)+s(9351)*(1/9)+aux(534) s(9359) =< aux(526)*(5/9)+s(9351)*(1/9)+aux(534) s(9360) =< aux(526)*(5/9)+s(9351)*(1/9)+aux(534) s(9361) =< aux(526)*(5/9)+s(9351)*(1/9)+aux(534) s(9362) =< aux(526)*(5/9)+s(9351)*(1/9)+aux(534) s(9363) =< aux(526)*(5/9)+s(9351)*(1/9)+aux(534) s(9365) =< aux(526)*(1/5)+aux(530) s(9357) =< aux(526)*(1/5)+aux(530) s(9364) =< aux(526)*(1/4)+aux(527) s(9365) =< aux(526)*(1/4)+aux(527) s(9357) =< aux(526)*(1/4)+aux(527) s(9366) =< aux(526)*(5/16)+aux(531) s(9364) =< aux(526)*(5/16)+aux(531) s(9365) =< aux(526)*(5/16)+aux(531) s(9357) =< aux(526)*(5/16)+aux(531) s(9373) =< s(9363)*s(9368) s(9374) =< s(9363)*s(9368) s(9375) =< s(9363)*s(9369) s(9376) =< s(9362)*s(9369) s(9377) =< s(9360)*s(9370) s(9378) =< s(9360)*s(9371) s(9379) =< s(9360)*s(9370) s(9380) =< s(9359)*s(9370) s(9381) =< s(9359)*s(9371) s(9382) =< s(9358)*s(9368) s(9383) =< s(9365)*s(9372) s(9384) =< s(9365)*s(9370) s(9385) =< s(9364)*s(9370) s(9386) =< s(9366)*s(9368) s(9387) =< s(9374) s(9388) =< s(9375) s(9389) =< s(9376) s(9390) =< s(9377) s(9391) =< s(9378) s(9392) =< s(9381) s(9393) =< s(9392)*s(9371) s(9394) =< s(9393)*s(9371) s(9395) =< s(9380) s(9396) =< s(9395)*aux(525) s(9397) =< s(9396) s(9398) =< s(9367) s(9399) =< s(9392)*s(9371) s(9400) =< s(9399) s(9401) =< s(9382) s(9402) =< s(9401)*s(9368) s(9403) =< s(9402)*s(9368) s(9404) =< s(9384) s(9405) =< s(9383) s(9406) =< s(9385) s(9407) =< s(9386) s(9408) =< s(9407)*s(9368) s(9542) =< aux(525) s(9410) =< aux(514) s(9411) =< s(9410)*aux(514) s(9412) =< s(9411) s(9294) =< aux(513) s(9295) =< aux(513) s(9296) =< aux(513) s(9297) =< aux(513) s(9298) =< aux(513) s(9299) =< aux(513) s(9300) =< aux(513) s(9288) =< aux(513) s(9288) =< aux(515) s(9301) =< aux(516) s(9297) =< aux(517) s(9302) =< aux(519) s(9303) =< aux(520) s(9299) =< aux(521) s(9304) =< aux(522) s(9296) =< aux(522) s(9295) =< aux(523) s(9305) =< aux(514)+1 s(9306) =< aux(514)+3 s(9307) =< aux(514) s(9308) =< aux(514)+2 s(9309) =< aux(514)-1 s(9299) =< aux(515)*(1/5)+aux(521) s(9300) =< aux(515)*(1/5)+aux(521) s(9297) =< aux(515)*(1/3)+aux(517) s(9298) =< aux(515)*(1/3)+aux(517) s(9299) =< aux(515)*(1/3)+aux(517) s(9300) =< aux(515)*(1/3)+aux(517) s(9296) =< aux(515)*(3/7)+aux(522) s(9297) =< aux(515)*(3/7)+aux(522) s(9298) =< aux(515)*(3/7)+aux(522) s(9299) =< aux(515)*(3/7)+aux(522) s(9300) =< aux(515)*(3/7)+aux(522) s(9304) =< aux(515)*(3/7)+aux(522) s(9295) =< aux(515)*(5/9)+s(9288)*(1/9)+aux(523) s(9296) =< aux(515)*(5/9)+s(9288)*(1/9)+aux(523) s(9297) =< aux(515)*(5/9)+s(9288)*(1/9)+aux(523) s(9298) =< aux(515)*(5/9)+s(9288)*(1/9)+aux(523) s(9299) =< aux(515)*(5/9)+s(9288)*(1/9)+aux(523) s(9300) =< aux(515)*(5/9)+s(9288)*(1/9)+aux(523) s(9302) =< aux(515)*(1/5)+aux(519) s(9294) =< aux(515)*(1/5)+aux(519) s(9301) =< aux(515)*(1/4)+aux(516) s(9302) =< aux(515)*(1/4)+aux(516) s(9294) =< aux(515)*(1/4)+aux(516) s(9303) =< aux(515)*(5/16)+aux(520) s(9301) =< aux(515)*(5/16)+aux(520) s(9302) =< aux(515)*(5/16)+aux(520) s(9294) =< aux(515)*(5/16)+aux(520) s(9310) =< s(9300)*s(9305) s(9311) =< s(9300)*s(9305) s(9312) =< s(9300)*s(9306) s(9313) =< s(9299)*s(9306) s(9314) =< s(9297)*s(9307) s(9315) =< s(9297)*s(9308) s(9316) =< s(9297)*s(9307) s(9317) =< s(9296)*s(9307) s(9318) =< s(9296)*s(9308) s(9319) =< s(9295)*s(9305) s(9320) =< s(9302)*s(9309) s(9321) =< s(9302)*s(9307) s(9322) =< s(9301)*s(9307) s(9323) =< s(9303)*s(9305) s(9324) =< s(9311) s(9325) =< s(9312) s(9326) =< s(9313) s(9327) =< s(9314) s(9328) =< s(9315) s(9329) =< s(9318) s(9330) =< s(9329)*s(9308) s(9331) =< s(9330)*s(9308) s(9332) =< s(9317) s(9333) =< s(9332)*aux(514) s(9334) =< s(9333) s(9335) =< s(9304) s(9336) =< s(9329)*s(9308) s(9337) =< s(9336) s(9338) =< s(9319) s(9339) =< s(9338)*s(9305) s(9340) =< s(9339)*s(9305) s(9341) =< s(9321) s(9342) =< s(9320) s(9343) =< s(9322) s(9344) =< s(9323) s(9345) =< s(9344)*s(9305) s(9675) =< aux(515) s(9675) =< aux(514) s(9676) =< s(9410)*aux(514) s(9677) =< s(9675) s(9678) =< s(9676)*aux(514) with precondition: [V>=1,Out>=1,2*V1>=Out+1] * Chain [82]: 1*s(9828)+5*s(9829)+8*s(9830)+6*s(9831)+1*s(9832)+3*s(9833)+3*s(9834)+4*s(9835)+4*s(9836)+4*s(9837)+1*s(9844)+1*s(9850)+2*s(9858)+2*s(9859)+8*s(9860)+3*s(9861)+2*s(9862)+23*s(9863)+4*s(9864)+1*s(9865)+6*s(9866)+6*s(9868)+2*s(9869)+6*s(9871)+12*s(9872)+3*s(9873)+1*s(9874)+2*s(9875)+2*s(9876)+8*s(9877)+7*s(9878)+1*s(9879)+2*s(9891)+10*s(9892)+16*s(9893)+12*s(9894)+2*s(9895)+6*s(9896)+6*s(9897)+8*s(9898)+8*s(9899)+8*s(9900)+2*s(9907)+2*s(9913)+4*s(9921)+4*s(9922)+16*s(9923)+6*s(9924)+4*s(9925)+46*s(9926)+8*s(9927)+2*s(9928)+12*s(9929)+12*s(9931)+4*s(9932)+12*s(9934)+24*s(9935)+6*s(9936)+2*s(9937)+4*s(9938)+4*s(9939)+16*s(9940)+14*s(9941)+2*s(9942)+8*s(9945)+4*s(9946)+6*s(9948)+8*s(10014)+6*s(10017)+5 Such that:s(10013) =< 2 s(9817) =< V1 aux(535) =< 2*V1 s(9819) =< 2*V1+1 s(9820) =< V1/2 s(9821) =< 2/3*V1 s(9822) =< 2/3*V1+1/3 s(9823) =< 3/5*V1 s(9824) =< 3/8*V1 s(9825) =< 4/5*V1 s(9826) =< 4/7*V1 s(9827) =< 4/9*V1 aux(536) =< 1 aux(537) =< V aux(538) =< 2*V aux(539) =< 2*V+1 aux(540) =< V/2 aux(541) =< 2/3*V aux(542) =< 2/3*V+1/3 aux(543) =< 3/5*V aux(544) =< 3/8*V aux(545) =< 4/5*V aux(546) =< 4/7*V aux(547) =< 4/9*V s(9885) =< aux(542) s(9945) =< aux(535) s(9946) =< aux(536) s(9947) =< s(9945)*aux(535) s(9948) =< s(9947) s(9891) =< aux(537) s(9892) =< aux(537) s(9893) =< aux(537) s(9894) =< aux(537) s(9895) =< aux(537) s(9896) =< aux(537) s(9897) =< aux(537) s(9885) =< aux(537) s(9885) =< aux(539) s(9898) =< aux(540) s(9894) =< aux(541) s(9899) =< aux(543) s(9900) =< aux(544) s(9896) =< aux(545) s(9901) =< aux(546) s(9893) =< aux(546) s(9892) =< aux(547) s(9902) =< aux(538)+1 s(9903) =< aux(538)+3 s(9904) =< aux(538) s(9905) =< aux(538)+2 s(9906) =< aux(538)-1 s(9896) =< aux(539)*(1/5)+aux(545) s(9897) =< aux(539)*(1/5)+aux(545) s(9894) =< aux(539)*(1/3)+aux(541) s(9895) =< aux(539)*(1/3)+aux(541) s(9896) =< aux(539)*(1/3)+aux(541) s(9897) =< aux(539)*(1/3)+aux(541) s(9893) =< aux(539)*(3/7)+aux(546) s(9894) =< aux(539)*(3/7)+aux(546) s(9895) =< aux(539)*(3/7)+aux(546) s(9896) =< aux(539)*(3/7)+aux(546) s(9897) =< aux(539)*(3/7)+aux(546) s(9901) =< aux(539)*(3/7)+aux(546) s(9892) =< aux(539)*(5/9)+s(9885)*(1/9)+aux(547) s(9893) =< aux(539)*(5/9)+s(9885)*(1/9)+aux(547) s(9894) =< aux(539)*(5/9)+s(9885)*(1/9)+aux(547) s(9895) =< aux(539)*(5/9)+s(9885)*(1/9)+aux(547) s(9896) =< aux(539)*(5/9)+s(9885)*(1/9)+aux(547) s(9897) =< aux(539)*(5/9)+s(9885)*(1/9)+aux(547) s(9899) =< aux(539)*(1/5)+aux(543) s(9891) =< aux(539)*(1/5)+aux(543) s(9898) =< aux(539)*(1/4)+aux(540) s(9899) =< aux(539)*(1/4)+aux(540) s(9891) =< aux(539)*(1/4)+aux(540) s(9900) =< aux(539)*(5/16)+aux(544) s(9898) =< aux(539)*(5/16)+aux(544) s(9899) =< aux(539)*(5/16)+aux(544) s(9891) =< aux(539)*(5/16)+aux(544) s(9907) =< s(9897)*s(9902) s(9908) =< s(9897)*s(9902) s(9909) =< s(9897)*s(9903) s(9910) =< s(9896)*s(9903) s(9911) =< s(9894)*s(9904) s(9912) =< s(9894)*s(9905) s(9913) =< s(9894)*s(9904) s(9914) =< s(9893)*s(9904) s(9915) =< s(9893)*s(9905) s(9916) =< s(9892)*s(9902) s(9917) =< s(9899)*s(9906) s(9918) =< s(9899)*s(9904) s(9919) =< s(9898)*s(9904) s(9920) =< s(9900)*s(9902) s(9921) =< s(9908) s(9922) =< s(9909) s(9923) =< s(9910) s(9924) =< s(9911) s(9925) =< s(9912) s(9926) =< s(9915) s(9927) =< s(9926)*s(9905) s(9928) =< s(9927)*s(9905) s(9929) =< s(9914) s(9930) =< s(9929)*aux(538) s(9931) =< s(9930) s(9932) =< s(9901) s(9933) =< s(9926)*s(9905) s(9934) =< s(9933) s(9935) =< s(9916) s(9936) =< s(9935)*s(9902) s(9937) =< s(9936)*s(9902) s(9938) =< s(9918) s(9939) =< s(9917) s(9940) =< s(9919) s(9941) =< s(9920) s(9942) =< s(9941)*s(9902) s(9828) =< s(9817) s(9829) =< s(9817) s(9830) =< s(9817) s(9831) =< s(9817) s(9832) =< s(9817) s(9833) =< s(9817) s(9834) =< s(9817) s(9822) =< s(9817) s(9822) =< s(9819) s(9835) =< s(9820) s(9831) =< s(9821) s(9836) =< s(9823) s(9837) =< s(9824) s(9833) =< s(9825) s(9838) =< s(9826) s(9830) =< s(9826) s(9829) =< s(9827) s(9839) =< aux(535)+1 s(9840) =< aux(535)+3 s(9841) =< aux(535) s(9842) =< aux(535)+2 s(9843) =< aux(535)-1 s(9833) =< s(9819)*(1/5)+s(9825) s(9834) =< s(9819)*(1/5)+s(9825) s(9831) =< s(9819)*(1/3)+s(9821) s(9832) =< s(9819)*(1/3)+s(9821) s(9833) =< s(9819)*(1/3)+s(9821) s(9834) =< s(9819)*(1/3)+s(9821) s(9830) =< s(9819)*(3/7)+s(9826) s(9831) =< s(9819)*(3/7)+s(9826) s(9832) =< s(9819)*(3/7)+s(9826) s(9833) =< s(9819)*(3/7)+s(9826) s(9834) =< s(9819)*(3/7)+s(9826) s(9838) =< s(9819)*(3/7)+s(9826) s(9829) =< s(9819)*(5/9)+s(9822)*(1/9)+s(9827) s(9830) =< s(9819)*(5/9)+s(9822)*(1/9)+s(9827) s(9831) =< s(9819)*(5/9)+s(9822)*(1/9)+s(9827) s(9832) =< s(9819)*(5/9)+s(9822)*(1/9)+s(9827) s(9833) =< s(9819)*(5/9)+s(9822)*(1/9)+s(9827) s(9834) =< s(9819)*(5/9)+s(9822)*(1/9)+s(9827) s(9836) =< s(9819)*(1/5)+s(9823) s(9828) =< s(9819)*(1/5)+s(9823) s(9835) =< s(9819)*(1/4)+s(9820) s(9836) =< s(9819)*(1/4)+s(9820) s(9828) =< s(9819)*(1/4)+s(9820) s(9837) =< s(9819)*(5/16)+s(9824) s(9835) =< s(9819)*(5/16)+s(9824) s(9836) =< s(9819)*(5/16)+s(9824) s(9828) =< s(9819)*(5/16)+s(9824) s(9844) =< s(9834)*s(9839) s(9845) =< s(9834)*s(9839) s(9846) =< s(9834)*s(9840) s(9847) =< s(9833)*s(9840) s(9848) =< s(9831)*s(9841) s(9849) =< s(9831)*s(9842) s(9850) =< s(9831)*s(9841) s(9851) =< s(9830)*s(9841) s(9852) =< s(9830)*s(9842) s(9853) =< s(9829)*s(9839) s(9854) =< s(9836)*s(9843) s(9855) =< s(9836)*s(9841) s(9856) =< s(9835)*s(9841) s(9857) =< s(9837)*s(9839) s(9858) =< s(9845) s(9859) =< s(9846) s(9860) =< s(9847) s(9861) =< s(9848) s(9862) =< s(9849) s(9863) =< s(9852) s(9864) =< s(9863)*s(9842) s(9865) =< s(9864)*s(9842) s(9866) =< s(9851) s(9867) =< s(9866)*aux(535) s(9868) =< s(9867) s(9869) =< s(9838) s(9870) =< s(9863)*s(9842) s(9871) =< s(9870) s(9872) =< s(9853) s(9873) =< s(9872)*s(9839) s(9874) =< s(9873)*s(9839) s(9875) =< s(9855) s(9876) =< s(9854) s(9877) =< s(9856) s(9878) =< s(9857) s(9879) =< s(9878)*s(9839) s(10014) =< s(10013) s(10016) =< s(10014)*s(10013) s(10017) =< s(10016) with precondition: [V>=1,Out>=2,2*V1>=Out] * Chain [81]: 1*s(10029)+5*s(10030)+8*s(10031)+6*s(10032)+1*s(10033)+3*s(10034)+3*s(10035)+4*s(10036)+4*s(10037)+4*s(10038)+1*s(10045)+1*s(10051)+2*s(10059)+2*s(10060)+8*s(10061)+3*s(10062)+2*s(10063)+23*s(10064)+4*s(10065)+1*s(10066)+6*s(10067)+6*s(10069)+2*s(10070)+6*s(10072)+12*s(10073)+3*s(10074)+1*s(10075)+2*s(10076)+2*s(10077)+8*s(10078)+7*s(10079)+1*s(10080)+1 Such that:s(10018) =< V1 s(10019) =< 2*V1 s(10020) =< 2*V1+1 s(10021) =< V1/2 s(10022) =< 2/3*V1 s(10023) =< 2/3*V1+1/3 s(10024) =< 3/5*V1 s(10025) =< 3/8*V1 s(10026) =< 4/5*V1 s(10027) =< 4/7*V1 s(10028) =< 4/9*V1 s(10029) =< s(10018) s(10030) =< s(10018) s(10031) =< s(10018) s(10032) =< s(10018) s(10033) =< s(10018) s(10034) =< s(10018) s(10035) =< s(10018) s(10023) =< s(10018) s(10023) =< s(10020) s(10036) =< s(10021) s(10032) =< s(10022) s(10037) =< s(10024) s(10038) =< s(10025) s(10034) =< s(10026) s(10039) =< s(10027) s(10031) =< s(10027) s(10030) =< s(10028) s(10040) =< s(10019)+1 s(10041) =< s(10019)+3 s(10042) =< s(10019) s(10043) =< s(10019)+2 s(10044) =< s(10019)-1 s(10034) =< s(10020)*(1/5)+s(10026) s(10035) =< s(10020)*(1/5)+s(10026) s(10032) =< s(10020)*(1/3)+s(10022) s(10033) =< s(10020)*(1/3)+s(10022) s(10034) =< s(10020)*(1/3)+s(10022) s(10035) =< s(10020)*(1/3)+s(10022) s(10031) =< s(10020)*(3/7)+s(10027) s(10032) =< s(10020)*(3/7)+s(10027) s(10033) =< s(10020)*(3/7)+s(10027) s(10034) =< s(10020)*(3/7)+s(10027) s(10035) =< s(10020)*(3/7)+s(10027) s(10039) =< s(10020)*(3/7)+s(10027) s(10030) =< s(10020)*(5/9)+s(10023)*(1/9)+s(10028) s(10031) =< s(10020)*(5/9)+s(10023)*(1/9)+s(10028) s(10032) =< s(10020)*(5/9)+s(10023)*(1/9)+s(10028) s(10033) =< s(10020)*(5/9)+s(10023)*(1/9)+s(10028) s(10034) =< s(10020)*(5/9)+s(10023)*(1/9)+s(10028) s(10035) =< s(10020)*(5/9)+s(10023)*(1/9)+s(10028) s(10037) =< s(10020)*(1/5)+s(10024) s(10029) =< s(10020)*(1/5)+s(10024) s(10036) =< s(10020)*(1/4)+s(10021) s(10037) =< s(10020)*(1/4)+s(10021) s(10029) =< s(10020)*(1/4)+s(10021) s(10038) =< s(10020)*(5/16)+s(10025) s(10036) =< s(10020)*(5/16)+s(10025) s(10037) =< s(10020)*(5/16)+s(10025) s(10029) =< s(10020)*(5/16)+s(10025) s(10045) =< s(10035)*s(10040) s(10046) =< s(10035)*s(10040) s(10047) =< s(10035)*s(10041) s(10048) =< s(10034)*s(10041) s(10049) =< s(10032)*s(10042) s(10050) =< s(10032)*s(10043) s(10051) =< s(10032)*s(10042) s(10052) =< s(10031)*s(10042) s(10053) =< s(10031)*s(10043) s(10054) =< s(10030)*s(10040) s(10055) =< s(10037)*s(10044) s(10056) =< s(10037)*s(10042) s(10057) =< s(10036)*s(10042) s(10058) =< s(10038)*s(10040) s(10059) =< s(10046) s(10060) =< s(10047) s(10061) =< s(10048) s(10062) =< s(10049) s(10063) =< s(10050) s(10064) =< s(10053) s(10065) =< s(10064)*s(10043) s(10066) =< s(10065)*s(10043) s(10067) =< s(10052) s(10068) =< s(10067)*s(10019) s(10069) =< s(10068) s(10070) =< s(10039) s(10071) =< s(10064)*s(10043) s(10072) =< s(10071) s(10073) =< s(10054) s(10074) =< s(10073)*s(10040) s(10075) =< s(10074)*s(10040) s(10076) =< s(10056) s(10077) =< s(10055) s(10078) =< s(10057) s(10079) =< s(10058) s(10080) =< s(10079)*s(10040) with precondition: [V=2,Out=0,V1>=0] * Chain [80]: 1*s(10092)+5*s(10093)+8*s(10094)+6*s(10095)+1*s(10096)+3*s(10097)+3*s(10098)+4*s(10099)+4*s(10100)+4*s(10101)+1*s(10108)+1*s(10114)+2*s(10122)+2*s(10123)+8*s(10124)+3*s(10125)+2*s(10126)+23*s(10127)+4*s(10128)+1*s(10129)+6*s(10130)+6*s(10132)+2*s(10133)+6*s(10135)+12*s(10136)+3*s(10137)+1*s(10138)+2*s(10139)+2*s(10140)+8*s(10141)+7*s(10142)+1*s(10143)+2*s(10146)+2*s(10147)+5 Such that:s(10145) =< 2 s(10081) =< V1 s(10083) =< 2*V1+1 s(10084) =< V1/2 s(10085) =< 2/3*V1 s(10086) =< 2/3*V1+1/3 s(10087) =< 3/5*V1 s(10088) =< 3/8*V1 s(10089) =< 4/5*V1 s(10090) =< 4/7*V1 s(10091) =< 4/9*V1 aux(548) =< 2*V1 s(10146) =< aux(548) s(10147) =< s(10145) s(10092) =< s(10081) s(10093) =< s(10081) s(10094) =< s(10081) s(10095) =< s(10081) s(10096) =< s(10081) s(10097) =< s(10081) s(10098) =< s(10081) s(10086) =< s(10081) s(10086) =< s(10083) s(10099) =< s(10084) s(10095) =< s(10085) s(10100) =< s(10087) s(10101) =< s(10088) s(10097) =< s(10089) s(10102) =< s(10090) s(10094) =< s(10090) s(10093) =< s(10091) s(10103) =< aux(548)+1 s(10104) =< aux(548)+3 s(10105) =< aux(548) s(10106) =< aux(548)+2 s(10107) =< aux(548)-1 s(10097) =< s(10083)*(1/5)+s(10089) s(10098) =< s(10083)*(1/5)+s(10089) s(10095) =< s(10083)*(1/3)+s(10085) s(10096) =< s(10083)*(1/3)+s(10085) s(10097) =< s(10083)*(1/3)+s(10085) s(10098) =< s(10083)*(1/3)+s(10085) s(10094) =< s(10083)*(3/7)+s(10090) s(10095) =< s(10083)*(3/7)+s(10090) s(10096) =< s(10083)*(3/7)+s(10090) s(10097) =< s(10083)*(3/7)+s(10090) s(10098) =< s(10083)*(3/7)+s(10090) s(10102) =< s(10083)*(3/7)+s(10090) s(10093) =< s(10083)*(5/9)+s(10086)*(1/9)+s(10091) s(10094) =< s(10083)*(5/9)+s(10086)*(1/9)+s(10091) s(10095) =< s(10083)*(5/9)+s(10086)*(1/9)+s(10091) s(10096) =< s(10083)*(5/9)+s(10086)*(1/9)+s(10091) s(10097) =< s(10083)*(5/9)+s(10086)*(1/9)+s(10091) s(10098) =< s(10083)*(5/9)+s(10086)*(1/9)+s(10091) s(10100) =< s(10083)*(1/5)+s(10087) s(10092) =< s(10083)*(1/5)+s(10087) s(10099) =< s(10083)*(1/4)+s(10084) s(10100) =< s(10083)*(1/4)+s(10084) s(10092) =< s(10083)*(1/4)+s(10084) s(10101) =< s(10083)*(5/16)+s(10088) s(10099) =< s(10083)*(5/16)+s(10088) s(10100) =< s(10083)*(5/16)+s(10088) s(10092) =< s(10083)*(5/16)+s(10088) s(10108) =< s(10098)*s(10103) s(10109) =< s(10098)*s(10103) s(10110) =< s(10098)*s(10104) s(10111) =< s(10097)*s(10104) s(10112) =< s(10095)*s(10105) s(10113) =< s(10095)*s(10106) s(10114) =< s(10095)*s(10105) s(10115) =< s(10094)*s(10105) s(10116) =< s(10094)*s(10106) s(10117) =< s(10093)*s(10103) s(10118) =< s(10100)*s(10107) s(10119) =< s(10100)*s(10105) s(10120) =< s(10099)*s(10105) s(10121) =< s(10101)*s(10103) s(10122) =< s(10109) s(10123) =< s(10110) s(10124) =< s(10111) s(10125) =< s(10112) s(10126) =< s(10113) s(10127) =< s(10116) s(10128) =< s(10127)*s(10106) s(10129) =< s(10128)*s(10106) s(10130) =< s(10115) s(10131) =< s(10130)*aux(548) s(10132) =< s(10131) s(10133) =< s(10102) s(10134) =< s(10127)*s(10106) s(10135) =< s(10134) s(10136) =< s(10117) s(10137) =< s(10136)*s(10103) s(10138) =< s(10137)*s(10103) s(10139) =< s(10119) s(10140) =< s(10118) s(10141) =< s(10120) s(10142) =< s(10121) s(10143) =< s(10142)*s(10103) with precondition: [V=2,Out=1,V1>=1] * Chain [79]: 2*s(10159)+10*s(10160)+16*s(10161)+12*s(10162)+2*s(10163)+6*s(10164)+6*s(10165)+8*s(10166)+8*s(10167)+8*s(10168)+2*s(10175)+2*s(10181)+4*s(10189)+4*s(10190)+16*s(10191)+6*s(10192)+4*s(10193)+46*s(10194)+8*s(10195)+2*s(10196)+12*s(10197)+12*s(10199)+4*s(10200)+12*s(10202)+24*s(10203)+6*s(10204)+2*s(10205)+4*s(10206)+4*s(10207)+16*s(10208)+14*s(10209)+2*s(10210)+1*s(10222)+5*s(10223)+8*s(10224)+6*s(10225)+1*s(10226)+3*s(10227)+3*s(10228)+4*s(10229)+4*s(10230)+4*s(10231)+1*s(10238)+1*s(10244)+2*s(10252)+2*s(10253)+8*s(10254)+3*s(10255)+2*s(10256)+23*s(10257)+4*s(10258)+1*s(10259)+6*s(10260)+6*s(10262)+2*s(10263)+6*s(10265)+12*s(10266)+3*s(10267)+1*s(10268)+2*s(10269)+2*s(10270)+8*s(10271)+7*s(10272)+1*s(10273)+4*s(10277)+3*s(10280)+8*s(10281)+1*s(10282)+4*s(10349)+3*s(10352)+1*s(10354)+1 Such that:s(10350) =< 2 s(10211) =< V s(10212) =< 2*V s(10213) =< 2*V+1 s(10214) =< V/2 s(10215) =< 2/3*V s(10216) =< 2/3*V+1/3 s(10217) =< 3/5*V s(10218) =< 3/8*V s(10219) =< 4/5*V s(10220) =< 4/7*V s(10221) =< 4/9*V aux(554) =< V1 aux(555) =< 2*V1 aux(556) =< 2*V1+1 aux(557) =< V1/2 aux(558) =< 2/3*V1 aux(559) =< 2/3*V1+1/3 aux(560) =< 3/5*V1 aux(561) =< 3/8*V1 aux(562) =< 4/5*V1 aux(563) =< 4/7*V1 aux(564) =< 4/9*V1 s(10153) =< aux(559) s(10349) =< aux(554) s(10279) =< aux(556) s(10279) =< aux(555) s(10352) =< s(10349)*aux(555) s(10281) =< s(10279) s(10354) =< s(10352)*s(10350) s(10159) =< aux(554) s(10160) =< aux(554) s(10161) =< aux(554) s(10162) =< aux(554) s(10163) =< aux(554) s(10164) =< aux(554) s(10165) =< aux(554) s(10153) =< aux(554) s(10153) =< aux(556) s(10166) =< aux(557) s(10162) =< aux(558) s(10167) =< aux(560) s(10168) =< aux(561) s(10164) =< aux(562) s(10169) =< aux(563) s(10161) =< aux(563) s(10160) =< aux(564) s(10170) =< aux(555)+1 s(10171) =< aux(555)+3 s(10172) =< aux(555) s(10173) =< aux(555)+2 s(10174) =< aux(555)-1 s(10164) =< aux(556)*(1/5)+aux(562) s(10165) =< aux(556)*(1/5)+aux(562) s(10162) =< aux(556)*(1/3)+aux(558) s(10163) =< aux(556)*(1/3)+aux(558) s(10164) =< aux(556)*(1/3)+aux(558) s(10165) =< aux(556)*(1/3)+aux(558) s(10161) =< aux(556)*(3/7)+aux(563) s(10162) =< aux(556)*(3/7)+aux(563) s(10163) =< aux(556)*(3/7)+aux(563) s(10164) =< aux(556)*(3/7)+aux(563) s(10165) =< aux(556)*(3/7)+aux(563) s(10169) =< aux(556)*(3/7)+aux(563) s(10160) =< aux(556)*(5/9)+s(10153)*(1/9)+aux(564) s(10161) =< aux(556)*(5/9)+s(10153)*(1/9)+aux(564) s(10162) =< aux(556)*(5/9)+s(10153)*(1/9)+aux(564) s(10163) =< aux(556)*(5/9)+s(10153)*(1/9)+aux(564) s(10164) =< aux(556)*(5/9)+s(10153)*(1/9)+aux(564) s(10165) =< aux(556)*(5/9)+s(10153)*(1/9)+aux(564) s(10167) =< aux(556)*(1/5)+aux(560) s(10159) =< aux(556)*(1/5)+aux(560) s(10166) =< aux(556)*(1/4)+aux(557) s(10167) =< aux(556)*(1/4)+aux(557) s(10159) =< aux(556)*(1/4)+aux(557) s(10168) =< aux(556)*(5/16)+aux(561) s(10166) =< aux(556)*(5/16)+aux(561) s(10167) =< aux(556)*(5/16)+aux(561) s(10159) =< aux(556)*(5/16)+aux(561) s(10175) =< s(10165)*s(10170) s(10176) =< s(10165)*s(10170) s(10177) =< s(10165)*s(10171) s(10178) =< s(10164)*s(10171) s(10179) =< s(10162)*s(10172) s(10180) =< s(10162)*s(10173) s(10181) =< s(10162)*s(10172) s(10182) =< s(10161)*s(10172) s(10183) =< s(10161)*s(10173) s(10184) =< s(10160)*s(10170) s(10185) =< s(10167)*s(10174) s(10186) =< s(10167)*s(10172) s(10187) =< s(10166)*s(10172) s(10188) =< s(10168)*s(10170) s(10189) =< s(10176) s(10190) =< s(10177) s(10191) =< s(10178) s(10192) =< s(10179) s(10193) =< s(10180) s(10194) =< s(10183) s(10195) =< s(10194)*s(10173) s(10196) =< s(10195)*s(10173) s(10197) =< s(10182) s(10198) =< s(10197)*aux(555) s(10199) =< s(10198) s(10200) =< s(10169) s(10201) =< s(10194)*s(10173) s(10202) =< s(10201) s(10203) =< s(10184) s(10204) =< s(10203)*s(10170) s(10205) =< s(10204)*s(10170) s(10206) =< s(10186) s(10207) =< s(10185) s(10208) =< s(10187) s(10209) =< s(10188) s(10210) =< s(10209)*s(10170) s(10277) =< aux(555) s(10280) =< s(10277)*aux(555) s(10282) =< s(10280)*aux(555) s(10222) =< s(10211) s(10223) =< s(10211) s(10224) =< s(10211) s(10225) =< s(10211) s(10226) =< s(10211) s(10227) =< s(10211) s(10228) =< s(10211) s(10216) =< s(10211) s(10216) =< s(10213) s(10229) =< s(10214) s(10225) =< s(10215) s(10230) =< s(10217) s(10231) =< s(10218) s(10227) =< s(10219) s(10232) =< s(10220) s(10224) =< s(10220) s(10223) =< s(10221) s(10233) =< s(10212)+1 s(10234) =< s(10212)+3 s(10235) =< s(10212) s(10236) =< s(10212)+2 s(10237) =< s(10212)-1 s(10227) =< s(10213)*(1/5)+s(10219) s(10228) =< s(10213)*(1/5)+s(10219) s(10225) =< s(10213)*(1/3)+s(10215) s(10226) =< s(10213)*(1/3)+s(10215) s(10227) =< s(10213)*(1/3)+s(10215) s(10228) =< s(10213)*(1/3)+s(10215) s(10224) =< s(10213)*(3/7)+s(10220) s(10225) =< s(10213)*(3/7)+s(10220) s(10226) =< s(10213)*(3/7)+s(10220) s(10227) =< s(10213)*(3/7)+s(10220) s(10228) =< s(10213)*(3/7)+s(10220) s(10232) =< s(10213)*(3/7)+s(10220) s(10223) =< s(10213)*(5/9)+s(10216)*(1/9)+s(10221) s(10224) =< s(10213)*(5/9)+s(10216)*(1/9)+s(10221) s(10225) =< s(10213)*(5/9)+s(10216)*(1/9)+s(10221) s(10226) =< s(10213)*(5/9)+s(10216)*(1/9)+s(10221) s(10227) =< s(10213)*(5/9)+s(10216)*(1/9)+s(10221) s(10228) =< s(10213)*(5/9)+s(10216)*(1/9)+s(10221) s(10230) =< s(10213)*(1/5)+s(10217) s(10222) =< s(10213)*(1/5)+s(10217) s(10229) =< s(10213)*(1/4)+s(10214) s(10230) =< s(10213)*(1/4)+s(10214) s(10222) =< s(10213)*(1/4)+s(10214) s(10231) =< s(10213)*(5/16)+s(10218) s(10229) =< s(10213)*(5/16)+s(10218) s(10230) =< s(10213)*(5/16)+s(10218) s(10222) =< s(10213)*(5/16)+s(10218) s(10238) =< s(10228)*s(10233) s(10239) =< s(10228)*s(10233) s(10240) =< s(10228)*s(10234) s(10241) =< s(10227)*s(10234) s(10242) =< s(10225)*s(10235) s(10243) =< s(10225)*s(10236) s(10244) =< s(10225)*s(10235) s(10245) =< s(10224)*s(10235) s(10246) =< s(10224)*s(10236) s(10247) =< s(10223)*s(10233) s(10248) =< s(10230)*s(10237) s(10249) =< s(10230)*s(10235) s(10250) =< s(10229)*s(10235) s(10251) =< s(10231)*s(10233) s(10252) =< s(10239) s(10253) =< s(10240) s(10254) =< s(10241) s(10255) =< s(10242) s(10256) =< s(10243) s(10257) =< s(10246) s(10258) =< s(10257)*s(10236) s(10259) =< s(10258)*s(10236) s(10260) =< s(10245) s(10261) =< s(10260)*s(10212) s(10262) =< s(10261) s(10263) =< s(10232) s(10264) =< s(10257)*s(10236) s(10265) =< s(10264) s(10266) =< s(10247) s(10267) =< s(10266)*s(10233) s(10268) =< s(10267)*s(10233) s(10269) =< s(10249) s(10270) =< s(10248) s(10271) =< s(10250) s(10272) =< s(10251) s(10273) =< s(10272)*s(10233) with precondition: [V>=1,Out>=1,2*V1>=2*Out+1] * Chain [78]: 1*s(10366)+5*s(10367)+8*s(10368)+6*s(10369)+1*s(10370)+3*s(10371)+3*s(10372)+4*s(10373)+4*s(10374)+4*s(10375)+1*s(10382)+1*s(10388)+2*s(10396)+2*s(10397)+8*s(10398)+3*s(10399)+2*s(10400)+23*s(10401)+4*s(10402)+1*s(10403)+6*s(10404)+6*s(10406)+2*s(10407)+6*s(10409)+12*s(10410)+3*s(10411)+1*s(10412)+2*s(10413)+2*s(10414)+8*s(10415)+7*s(10416)+1*s(10417)+6*s(10422)+2*s(10423)+3*s(10425)+4*s(10426)+1*s(10427)+5 Such that:s(10421) =< 2 s(10355) =< V1 s(10358) =< V1/2 s(10359) =< 2/3*V1 s(10360) =< 2/3*V1+1/3 s(10361) =< 3/5*V1 s(10362) =< 3/8*V1 s(10363) =< 4/5*V1 s(10364) =< 4/7*V1 s(10365) =< 4/9*V1 aux(565) =< 2*V1 aux(566) =< 2*V1+1 s(10422) =< aux(565) s(10423) =< s(10421) s(10424) =< aux(566) s(10424) =< aux(565) s(10425) =< s(10422)*aux(565) s(10426) =< s(10424) s(10427) =< s(10425)*s(10421) s(10366) =< s(10355) s(10367) =< s(10355) s(10368) =< s(10355) s(10369) =< s(10355) s(10370) =< s(10355) s(10371) =< s(10355) s(10372) =< s(10355) s(10360) =< s(10355) s(10360) =< aux(566) s(10373) =< s(10358) s(10369) =< s(10359) s(10374) =< s(10361) s(10375) =< s(10362) s(10371) =< s(10363) s(10376) =< s(10364) s(10368) =< s(10364) s(10367) =< s(10365) s(10377) =< aux(565)+1 s(10378) =< aux(565)+3 s(10379) =< aux(565) s(10380) =< aux(565)+2 s(10381) =< aux(565)-1 s(10371) =< aux(566)*(1/5)+s(10363) s(10372) =< aux(566)*(1/5)+s(10363) s(10369) =< aux(566)*(1/3)+s(10359) s(10370) =< aux(566)*(1/3)+s(10359) s(10371) =< aux(566)*(1/3)+s(10359) s(10372) =< aux(566)*(1/3)+s(10359) s(10368) =< aux(566)*(3/7)+s(10364) s(10369) =< aux(566)*(3/7)+s(10364) s(10370) =< aux(566)*(3/7)+s(10364) s(10371) =< aux(566)*(3/7)+s(10364) s(10372) =< aux(566)*(3/7)+s(10364) s(10376) =< aux(566)*(3/7)+s(10364) s(10367) =< aux(566)*(5/9)+s(10360)*(1/9)+s(10365) s(10368) =< aux(566)*(5/9)+s(10360)*(1/9)+s(10365) s(10369) =< aux(566)*(5/9)+s(10360)*(1/9)+s(10365) s(10370) =< aux(566)*(5/9)+s(10360)*(1/9)+s(10365) s(10371) =< aux(566)*(5/9)+s(10360)*(1/9)+s(10365) s(10372) =< aux(566)*(5/9)+s(10360)*(1/9)+s(10365) s(10374) =< aux(566)*(1/5)+s(10361) s(10366) =< aux(566)*(1/5)+s(10361) s(10373) =< aux(566)*(1/4)+s(10358) s(10374) =< aux(566)*(1/4)+s(10358) s(10366) =< aux(566)*(1/4)+s(10358) s(10375) =< aux(566)*(5/16)+s(10362) s(10373) =< aux(566)*(5/16)+s(10362) s(10374) =< aux(566)*(5/16)+s(10362) s(10366) =< aux(566)*(5/16)+s(10362) s(10382) =< s(10372)*s(10377) s(10383) =< s(10372)*s(10377) s(10384) =< s(10372)*s(10378) s(10385) =< s(10371)*s(10378) s(10386) =< s(10369)*s(10379) s(10387) =< s(10369)*s(10380) s(10388) =< s(10369)*s(10379) s(10389) =< s(10368)*s(10379) s(10390) =< s(10368)*s(10380) s(10391) =< s(10367)*s(10377) s(10392) =< s(10374)*s(10381) s(10393) =< s(10374)*s(10379) s(10394) =< s(10373)*s(10379) s(10395) =< s(10375)*s(10377) s(10396) =< s(10383) s(10397) =< s(10384) s(10398) =< s(10385) s(10399) =< s(10386) s(10400) =< s(10387) s(10401) =< s(10390) s(10402) =< s(10401)*s(10380) s(10403) =< s(10402)*s(10380) s(10404) =< s(10389) s(10405) =< s(10404)*aux(565) s(10406) =< s(10405) s(10407) =< s(10376) s(10408) =< s(10401)*s(10380) s(10409) =< s(10408) s(10410) =< s(10391) s(10411) =< s(10410)*s(10377) s(10412) =< s(10411)*s(10377) s(10413) =< s(10393) s(10414) =< s(10392) s(10415) =< s(10394) s(10416) =< s(10395) s(10417) =< s(10416)*s(10377) with precondition: [V=2,Out>=2,2*V1+1>=2*Out] #### Cost of chains of start(V1,V,V2): * Chain [85]: 25*s(11033)+4*s(11034)+1*s(11044)+42*s(11047)+1*s(11061)+12*s(11065)+36*s(11069)+4*s(11079)+3*s(11082)+8*s(11083)+1*s(11084)+3*s(11092)+1*s(11094)+59*s(11106)+295*s(11107)+472*s(11108)+354*s(11109)+59*s(11110)+177*s(11111)+177*s(11112)+236*s(11113)+236*s(11114)+236*s(11115)+59*s(11122)+59*s(11128)+118*s(11136)+118*s(11137)+472*s(11138)+177*s(11139)+118*s(11140)+1357*s(11141)+236*s(11142)+59*s(11143)+354*s(11144)+354*s(11146)+118*s(11147)+354*s(11149)+708*s(11150)+177*s(11151)+59*s(11152)+118*s(11153)+118*s(11154)+472*s(11155)+413*s(11156)+59*s(11157)+63*s(11181)+48*s(11184)+51*s(11185)+255*s(11186)+408*s(11187)+306*s(11188)+51*s(11189)+153*s(11190)+153*s(11191)+204*s(11192)+204*s(11193)+204*s(11194)+51*s(11201)+51*s(11207)+102*s(11215)+102*s(11216)+408*s(11217)+153*s(11218)+102*s(11219)+1173*s(11220)+204*s(11221)+51*s(11222)+306*s(11223)+306*s(11225)+102*s(11226)+306*s(11228)+612*s(11229)+153*s(11230)+51*s(11231)+102*s(11232)+102*s(11233)+408*s(11234)+357*s(11235)+51*s(11236)+71*s(11419)+10*s(11879)+1*s(11880)+1*s(11881)+18*s(11917)+90*s(11918)+144*s(11919)+108*s(11920)+18*s(11921)+54*s(11922)+54*s(11923)+72*s(11924)+72*s(11925)+72*s(11926)+18*s(11933)+18*s(11939)+36*s(11947)+36*s(11948)+144*s(11949)+54*s(11950)+36*s(11951)+414*s(11952)+72*s(11953)+18*s(11954)+108*s(11955)+108*s(11957)+36*s(11958)+108*s(11960)+216*s(11961)+54*s(11962)+18*s(11963)+36*s(11964)+36*s(11965)+144*s(11966)+126*s(11967)+18*s(11968)+4*s(12347)+1*s(12596)+1*s(12598)+12*s(12807)+12*s(12862)+16*s(12865)+2*s(12866)+1*s(12897)+3*s(13034)+1*s(13036)+5 Such that:s(11079) =< V1/2-V/2 aux(606) =< 1 aux(607) =< 2 aux(608) =< V1 aux(609) =< V1+1 aux(610) =< V1-V aux(611) =< 2*V1 aux(612) =< 2*V1+1 aux(613) =< V1/2 aux(614) =< 2/3*V1 aux(615) =< 2/3*V1+1/3 aux(616) =< 3/5*V1 aux(617) =< 3/8*V1 aux(618) =< 4/5*V1 aux(619) =< 4/7*V1 aux(620) =< 4/9*V1 aux(621) =< V aux(622) =< 2*V aux(623) =< 2*V+1 aux(624) =< V/2 aux(625) =< 2/3*V aux(626) =< 2/3*V+1/3 aux(627) =< 3/5*V aux(628) =< 3/8*V aux(629) =< 4/5*V aux(630) =< 4/7*V aux(631) =< 4/9*V aux(632) =< V2 aux(633) =< 2*V2 aux(634) =< 2*V2+1 aux(635) =< V2/2 aux(636) =< 2/3*V2 aux(637) =< 2/3*V2+1/3 aux(638) =< 3/5*V2 aux(639) =< 3/8*V2 aux(640) =< 4/5*V2 aux(641) =< 4/7*V2 aux(642) =< 4/9*V2 s(11069) =< aux(606) s(11181) =< aux(607) s(11047) =< aux(608) s(11100) =< aux(615) s(11033) =< aux(621) s(11183) =< aux(626) s(11064) =< s(11047)*aux(608) s(11065) =< s(11064) s(11185) =< aux(621) s(11186) =< aux(621) s(11187) =< aux(621) s(11188) =< aux(621) s(11189) =< aux(621) s(11190) =< aux(621) s(11191) =< aux(621) s(11183) =< aux(621) s(11183) =< aux(623) s(11192) =< aux(624) s(11188) =< aux(625) s(11193) =< aux(627) s(11194) =< aux(628) s(11190) =< aux(629) s(11195) =< aux(630) s(11187) =< aux(630) s(11186) =< aux(631) s(11196) =< aux(622)+1 s(11197) =< aux(622)+3 s(11198) =< aux(622) s(11199) =< aux(622)+2 s(11200) =< aux(622)-1 s(11190) =< aux(623)*(1/5)+aux(629) s(11191) =< aux(623)*(1/5)+aux(629) s(11188) =< aux(623)*(1/3)+aux(625) s(11189) =< aux(623)*(1/3)+aux(625) s(11190) =< aux(623)*(1/3)+aux(625) s(11191) =< aux(623)*(1/3)+aux(625) s(11187) =< aux(623)*(3/7)+aux(630) s(11188) =< aux(623)*(3/7)+aux(630) s(11189) =< aux(623)*(3/7)+aux(630) s(11190) =< aux(623)*(3/7)+aux(630) s(11191) =< aux(623)*(3/7)+aux(630) s(11195) =< aux(623)*(3/7)+aux(630) s(11186) =< aux(623)*(5/9)+s(11183)*(1/9)+aux(631) s(11187) =< aux(623)*(5/9)+s(11183)*(1/9)+aux(631) s(11188) =< aux(623)*(5/9)+s(11183)*(1/9)+aux(631) s(11189) =< aux(623)*(5/9)+s(11183)*(1/9)+aux(631) s(11190) =< aux(623)*(5/9)+s(11183)*(1/9)+aux(631) s(11191) =< aux(623)*(5/9)+s(11183)*(1/9)+aux(631) s(11193) =< aux(623)*(1/5)+aux(627) s(11185) =< aux(623)*(1/5)+aux(627) s(11192) =< aux(623)*(1/4)+aux(624) s(11193) =< aux(623)*(1/4)+aux(624) s(11185) =< aux(623)*(1/4)+aux(624) s(11194) =< aux(623)*(5/16)+aux(628) s(11192) =< aux(623)*(5/16)+aux(628) s(11193) =< aux(623)*(5/16)+aux(628) s(11185) =< aux(623)*(5/16)+aux(628) s(11201) =< s(11191)*s(11196) s(11202) =< s(11191)*s(11196) s(11203) =< s(11191)*s(11197) s(11204) =< s(11190)*s(11197) s(11205) =< s(11188)*s(11198) s(11206) =< s(11188)*s(11199) s(11207) =< s(11188)*s(11198) s(11208) =< s(11187)*s(11198) s(11209) =< s(11187)*s(11199) s(11210) =< s(11186)*s(11196) s(11211) =< s(11193)*s(11200) s(11212) =< s(11193)*s(11198) s(11213) =< s(11192)*s(11198) s(11214) =< s(11194)*s(11196) s(11215) =< s(11202) s(11216) =< s(11203) s(11217) =< s(11204) s(11218) =< s(11205) s(11219) =< s(11206) s(11220) =< s(11209) s(11221) =< s(11220)*s(11199) s(11222) =< s(11221)*s(11199) s(11223) =< s(11208) s(11224) =< s(11223)*aux(622) s(11225) =< s(11224) s(11226) =< s(11195) s(11227) =< s(11220)*s(11199) s(11228) =< s(11227) s(11229) =< s(11210) s(11230) =< s(11229)*s(11196) s(11231) =< s(11230)*s(11196) s(11232) =< s(11212) s(11233) =< s(11211) s(11234) =< s(11213) s(11235) =< s(11214) s(11236) =< s(11235)*s(11196) s(11106) =< aux(608) s(11107) =< aux(608) s(11108) =< aux(608) s(11109) =< aux(608) s(11110) =< aux(608) s(11111) =< aux(608) s(11112) =< aux(608) s(11100) =< aux(608) s(11100) =< aux(612) s(11113) =< aux(613) s(11109) =< aux(614) s(11114) =< aux(616) s(11115) =< aux(617) s(11111) =< aux(618) s(11116) =< aux(619) s(11108) =< aux(619) s(11107) =< aux(620) s(11117) =< aux(611)+1 s(11118) =< aux(611)+3 s(11119) =< aux(611) s(11120) =< aux(611)+2 s(11121) =< aux(611)-1 s(11111) =< aux(612)*(1/5)+aux(618) s(11112) =< aux(612)*(1/5)+aux(618) s(11109) =< aux(612)*(1/3)+aux(614) s(11110) =< aux(612)*(1/3)+aux(614) s(11111) =< aux(612)*(1/3)+aux(614) s(11112) =< aux(612)*(1/3)+aux(614) s(11108) =< aux(612)*(3/7)+aux(619) s(11109) =< aux(612)*(3/7)+aux(619) s(11110) =< aux(612)*(3/7)+aux(619) s(11111) =< aux(612)*(3/7)+aux(619) s(11112) =< aux(612)*(3/7)+aux(619) s(11116) =< aux(612)*(3/7)+aux(619) s(11107) =< aux(612)*(5/9)+s(11100)*(1/9)+aux(620) s(11108) =< aux(612)*(5/9)+s(11100)*(1/9)+aux(620) s(11109) =< aux(612)*(5/9)+s(11100)*(1/9)+aux(620) s(11110) =< aux(612)*(5/9)+s(11100)*(1/9)+aux(620) s(11111) =< aux(612)*(5/9)+s(11100)*(1/9)+aux(620) s(11112) =< aux(612)*(5/9)+s(11100)*(1/9)+aux(620) s(11114) =< aux(612)*(1/5)+aux(616) s(11106) =< aux(612)*(1/5)+aux(616) s(11113) =< aux(612)*(1/4)+aux(613) s(11114) =< aux(612)*(1/4)+aux(613) s(11106) =< aux(612)*(1/4)+aux(613) s(11115) =< aux(612)*(5/16)+aux(617) s(11113) =< aux(612)*(5/16)+aux(617) s(11114) =< aux(612)*(5/16)+aux(617) s(11106) =< aux(612)*(5/16)+aux(617) s(11122) =< s(11112)*s(11117) s(11123) =< s(11112)*s(11117) s(11124) =< s(11112)*s(11118) s(11125) =< s(11111)*s(11118) s(11126) =< s(11109)*s(11119) s(11127) =< s(11109)*s(11120) s(11128) =< s(11109)*s(11119) s(11129) =< s(11108)*s(11119) s(11130) =< s(11108)*s(11120) s(11131) =< s(11107)*s(11117) s(11132) =< s(11114)*s(11121) s(11133) =< s(11114)*s(11119) s(11134) =< s(11113)*s(11119) s(11135) =< s(11115)*s(11117) s(11136) =< s(11123) s(11137) =< s(11124) s(11138) =< s(11125) s(11139) =< s(11126) s(11140) =< s(11127) s(11141) =< s(11130) s(11142) =< s(11141)*s(11120) s(11143) =< s(11142)*s(11120) s(11144) =< s(11129) s(11145) =< s(11144)*aux(611) s(11146) =< s(11145) s(11147) =< s(11116) s(11148) =< s(11141)*s(11120) s(11149) =< s(11148) s(11150) =< s(11131) s(11151) =< s(11150)*s(11117) s(11152) =< s(11151)*s(11117) s(11153) =< s(11133) s(11154) =< s(11132) s(11155) =< s(11134) s(11156) =< s(11135) s(11157) =< s(11156)*s(11117) s(11419) =< aux(611) s(11879) =< s(11419)*aux(611) s(11880) =< s(11069)*aux(606) s(11881) =< s(11419)*aux(607) s(11184) =< aux(622) s(11916) =< aux(637) s(12347) =< aux(633) s(11917) =< aux(632) s(11918) =< aux(632) s(11919) =< aux(632) s(11920) =< aux(632) s(11921) =< aux(632) s(11922) =< aux(632) s(11923) =< aux(632) s(11916) =< aux(632) s(11916) =< aux(634) s(11924) =< aux(635) s(11920) =< aux(636) s(11925) =< aux(638) s(11926) =< aux(639) s(11922) =< aux(640) s(11927) =< aux(641) s(11919) =< aux(641) s(11918) =< aux(642) s(11928) =< aux(633)+1 s(11929) =< aux(633)+3 s(11930) =< aux(633) s(11931) =< aux(633)+2 s(11932) =< aux(633)-1 s(11922) =< aux(634)*(1/5)+aux(640) s(11923) =< aux(634)*(1/5)+aux(640) s(11920) =< aux(634)*(1/3)+aux(636) s(11921) =< aux(634)*(1/3)+aux(636) s(11922) =< aux(634)*(1/3)+aux(636) s(11923) =< aux(634)*(1/3)+aux(636) s(11919) =< aux(634)*(3/7)+aux(641) s(11920) =< aux(634)*(3/7)+aux(641) s(11921) =< aux(634)*(3/7)+aux(641) s(11922) =< aux(634)*(3/7)+aux(641) s(11923) =< aux(634)*(3/7)+aux(641) s(11927) =< aux(634)*(3/7)+aux(641) s(11918) =< aux(634)*(5/9)+s(11916)*(1/9)+aux(642) s(11919) =< aux(634)*(5/9)+s(11916)*(1/9)+aux(642) s(11920) =< aux(634)*(5/9)+s(11916)*(1/9)+aux(642) s(11921) =< aux(634)*(5/9)+s(11916)*(1/9)+aux(642) s(11922) =< aux(634)*(5/9)+s(11916)*(1/9)+aux(642) s(11923) =< aux(634)*(5/9)+s(11916)*(1/9)+aux(642) s(11925) =< aux(634)*(1/5)+aux(638) s(11917) =< aux(634)*(1/5)+aux(638) s(11924) =< aux(634)*(1/4)+aux(635) s(11925) =< aux(634)*(1/4)+aux(635) s(11917) =< aux(634)*(1/4)+aux(635) s(11926) =< aux(634)*(5/16)+aux(639) s(11924) =< aux(634)*(5/16)+aux(639) s(11925) =< aux(634)*(5/16)+aux(639) s(11917) =< aux(634)*(5/16)+aux(639) s(11933) =< s(11923)*s(11928) s(11934) =< s(11923)*s(11928) s(11935) =< s(11923)*s(11929) s(11936) =< s(11922)*s(11929) s(11937) =< s(11920)*s(11930) s(11938) =< s(11920)*s(11931) s(11939) =< s(11920)*s(11930) s(11940) =< s(11919)*s(11930) s(11941) =< s(11919)*s(11931) s(11942) =< s(11918)*s(11928) s(11943) =< s(11925)*s(11932) s(11944) =< s(11925)*s(11930) s(11945) =< s(11924)*s(11930) s(11946) =< s(11926)*s(11928) s(11947) =< s(11934) s(11948) =< s(11935) s(11949) =< s(11936) s(11950) =< s(11937) s(11951) =< s(11938) s(11952) =< s(11941) s(11953) =< s(11952)*s(11931) s(11954) =< s(11953)*s(11931) s(11955) =< s(11940) s(11956) =< s(11955)*aux(633) s(11957) =< s(11956) s(11958) =< s(11927) s(11959) =< s(11952)*s(11931) s(11960) =< s(11959) s(11961) =< s(11942) s(11962) =< s(11961)*s(11928) s(11963) =< s(11962)*s(11928) s(11964) =< s(11944) s(11965) =< s(11943) s(11966) =< s(11945) s(11967) =< s(11946) s(11968) =< s(11967)*s(11928) s(12596) =< s(11184)*aux(622) s(12598) =< s(11184)*aux(607) s(12863) =< aux(612) s(12863) =< aux(611) s(12865) =< s(12863) s(12897) =< s(11879)*aux(607) s(12861) =< s(11419)*aux(611) s(12862) =< s(12861) s(12806) =< s(11181)*aux(607) s(12807) =< s(12806) s(12866) =< s(11879)*aux(611) s(13034) =< s(11047)*aux(611) s(13036) =< s(13034)*aux(607) s(11081) =< aux(609) s(11081) =< aux(608) s(11082) =< s(11079)*aux(610) s(11083) =< s(11081) s(11084) =< s(11082)*aux(621) s(11092) =< s(11047)*aux(610) s(11094) =< s(11092)*aux(621) s(11034) =< aux(632) s(11061) =< s(11047)*aux(621) s(11044) =< s(11033)*aux(632) with precondition: [] Closed-form bounds of start(V1,V,V2): ------------------------------------- * Chain [85] with precondition: [] - Upper bound: nat(V1)*10308+216+nat(V1)*12*nat(V1)+nat(V)*nat(V1)+nat(V)*nat(V1)*nat(V1-V)+nat(V1)*7144*nat(2*V1)+nat(V1)*1652*nat(2*V1)*nat(2*V1)+nat(V1)*118*nat(2*V1)*nat(2*V1)*nat(2*V1)+nat(V1)*3*nat(V1-V)+nat(V)*8899+nat(V2)*nat(V)+nat(V)*6171*nat(2*V)+nat(V)*1428*nat(2*V)*nat(2*V)+nat(V)*102*nat(2*V)*nat(2*V)*nat(2*V)+nat(V1-V)*nat(V)*nat(V1/2-V/2)+nat(V2)*3136+nat(V2)*2178*nat(2*V2)+nat(V2)*504*nat(2*V2)*nat(2*V2)+nat(V2)*36*nat(2*V2)*nat(2*V2)*nat(2*V2)+nat(nat(2*V1)+ -1)*118*nat(3/5*V1)+nat(nat(2*V)+ -1)*102*nat(3/5*V)+nat(nat(2*V2)+ -1)*36*nat(3/5*V2)+nat(2*V1)*73+nat(2*V1)*24*nat(2*V1)+nat(2*V1)*2*nat(2*V1)*nat(2*V1)+nat(2*V1)*59*nat(2*V1)*nat(3/8*V1)+nat(2*V1)*118*nat(3/5*V1)+nat(2*V1)*531*nat(3/8*V1)+nat(2*V1)*472*nat(V1/2)+nat(2*V)*50+nat(2*V)*nat(2*V)+nat(2*V)*51*nat(2*V)*nat(3/8*V)+nat(2*V)*102*nat(3/5*V)+nat(2*V)*459*nat(3/8*V)+nat(2*V)*408*nat(V/2)+nat(2*V2)*4+nat(2*V2)*18*nat(2*V2)*nat(3/8*V2)+nat(2*V2)*36*nat(3/5*V2)+nat(2*V2)*162*nat(3/8*V2)+nat(2*V2)*144*nat(V2/2)+nat(3/5*V1)*236+nat(3/5*V)*204+nat(3/5*V2)*72+nat(3/8*V1)*708+nat(3/8*V)*612+nat(3/8*V2)*216+nat(4/7*V1)*118+nat(4/7*V)*102+nat(4/7*V2)*36+nat(V1+1)*8+nat(2*V1+1)*16+nat(V1-V)*3*nat(V1/2-V/2)+nat(V1/2-V/2)*4+nat(V1/2)*236+nat(V/2)*204+nat(V2/2)*72 - Complexity: n^4 ### Maximum cost of start(V1,V,V2): nat(V1)*10308+216+nat(V1)*12*nat(V1)+nat(V)*nat(V1)+nat(V)*nat(V1)*nat(V1-V)+nat(V1)*7144*nat(2*V1)+nat(V1)*1652*nat(2*V1)*nat(2*V1)+nat(V1)*118*nat(2*V1)*nat(2*V1)*nat(2*V1)+nat(V1)*3*nat(V1-V)+nat(V)*8899+nat(V2)*nat(V)+nat(V)*6171*nat(2*V)+nat(V)*1428*nat(2*V)*nat(2*V)+nat(V)*102*nat(2*V)*nat(2*V)*nat(2*V)+nat(V1-V)*nat(V)*nat(V1/2-V/2)+nat(V2)*3136+nat(V2)*2178*nat(2*V2)+nat(V2)*504*nat(2*V2)*nat(2*V2)+nat(V2)*36*nat(2*V2)*nat(2*V2)*nat(2*V2)+nat(nat(2*V1)+ -1)*118*nat(3/5*V1)+nat(nat(2*V)+ -1)*102*nat(3/5*V)+nat(nat(2*V2)+ -1)*36*nat(3/5*V2)+nat(2*V1)*73+nat(2*V1)*24*nat(2*V1)+nat(2*V1)*2*nat(2*V1)*nat(2*V1)+nat(2*V1)*59*nat(2*V1)*nat(3/8*V1)+nat(2*V1)*118*nat(3/5*V1)+nat(2*V1)*531*nat(3/8*V1)+nat(2*V1)*472*nat(V1/2)+nat(2*V)*50+nat(2*V)*nat(2*V)+nat(2*V)*51*nat(2*V)*nat(3/8*V)+nat(2*V)*102*nat(3/5*V)+nat(2*V)*459*nat(3/8*V)+nat(2*V)*408*nat(V/2)+nat(2*V2)*4+nat(2*V2)*18*nat(2*V2)*nat(3/8*V2)+nat(2*V2)*36*nat(3/5*V2)+nat(2*V2)*162*nat(3/8*V2)+nat(2*V2)*144*nat(V2/2)+nat(3/5*V1)*236+nat(3/5*V)*204+nat(3/5*V2)*72+nat(3/8*V1)*708+nat(3/8*V)*612+nat(3/8*V2)*216+nat(4/7*V1)*118+nat(4/7*V)*102+nat(4/7*V2)*36+nat(V1+1)*8+nat(2*V1+1)*16+nat(V1-V)*3*nat(V1/2-V/2)+nat(V1/2-V/2)*4+nat(V1/2)*236+nat(V/2)*204+nat(V2/2)*72 Asymptotic class: n^4 * Total analysis performed in 70009 ms. ---------------------------------------- (14) BOUNDS(1, n^4) ---------------------------------------- (15) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: le(0', Y) -> true le(s(X), 0') -> false le(s(X), s(Y)) -> le(X, Y) minus(0', Y) -> 0' minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0' ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0', s(Y)) -> 0' quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) The (relative) TRS S consists of the following rules: encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (17) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (18) Obligation: Innermost TRS: Rules: le(0', Y) -> true le(s(X), 0') -> false le(s(X), s(Y)) -> le(X, Y) minus(0', Y) -> 0' minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0' ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0', s(Y)) -> 0' quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) Types: le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot 0' :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encArg :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_0 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot hole_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot1_4 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4 :: Nat -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot ---------------------------------------- (19) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: le, minus, ifMinus, quot, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus = ifMinus minus < quot minus < encArg ifMinus < encArg quot < encArg ---------------------------------------- (20) Obligation: Innermost TRS: Rules: le(0', Y) -> true le(s(X), 0') -> false le(s(X), s(Y)) -> le(X, Y) minus(0', Y) -> 0' minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0' ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0', s(Y)) -> 0' quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) Types: le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot 0' :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encArg :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_0 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot hole_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot1_4 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4 :: Nat -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot Generator Equations: gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(0) <=> 0' gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(+(x, 1)) <=> s(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(x)) The following defined symbols remain to be analysed: le, minus, ifMinus, quot, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus = ifMinus minus < quot minus < encArg ifMinus < encArg quot < encArg ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: le(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n4_4), gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Induction Base: le(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(0), gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(0)) ->_R^Omega(1) true Induction Step: le(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(+(n4_4, 1)), gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(+(n4_4, 1))) ->_R^Omega(1) le(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n4_4), gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n4_4)) ->_IH true We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: le(0', Y) -> true le(s(X), 0') -> false le(s(X), s(Y)) -> le(X, Y) minus(0', Y) -> 0' minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0' ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0', s(Y)) -> 0' quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) Types: le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot 0' :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encArg :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_0 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot hole_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot1_4 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4 :: Nat -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot Generator Equations: gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(0) <=> 0' gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(+(x, 1)) <=> s(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(x)) The following defined symbols remain to be analysed: le, minus, ifMinus, quot, encArg They will be analysed ascendingly in the following order: le < minus le < encArg minus = ifMinus minus < quot minus < encArg ifMinus < encArg quot < encArg ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: le(0', Y) -> true le(s(X), 0') -> false le(s(X), s(Y)) -> le(X, Y) minus(0', Y) -> 0' minus(s(X), Y) -> ifMinus(le(s(X), Y), s(X), Y) ifMinus(true, s(X), Y) -> 0' ifMinus(false, s(X), Y) -> s(minus(X, Y)) quot(0', s(Y)) -> 0' quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) encArg(0') -> 0' encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_ifMinus(x_1, x_2, x_3)) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_ifMinus(x_1, x_2, x_3) -> ifMinus(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) Types: le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot 0' :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encArg :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot cons_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_le :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_0 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_true :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_s :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_false :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_minus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_ifMinus :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot encode_quot :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot hole_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot1_4 :: 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4 :: Nat -> 0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot Lemmas: le(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n4_4), gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n4_4)) -> true, rt in Omega(1 + n4_4) Generator Equations: gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(0) <=> 0' gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(+(x, 1)) <=> s(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(x)) The following defined symbols remain to be analysed: ifMinus, minus, quot, encArg They will be analysed ascendingly in the following order: minus = ifMinus minus < quot minus < encArg ifMinus < encArg quot < encArg ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n701_4)) -> gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n701_4), rt in Omega(0) Induction Base: encArg(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(0)) ->_R^Omega(0) 0' Induction Step: encArg(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(+(n701_4, 1))) ->_R^Omega(0) s(encArg(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(n701_4))) ->_IH s(gen_0':true:s:false:cons_le:cons_minus:cons_ifMinus:cons_quot2_4(c702_4)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (28) BOUNDS(1, INF)